A good friend and colleague who teaches biology teaches his students about the spectrum of certainty. He tries to get them to that all the ideas they’re studying in class, consider the evidence, and put them somewhere along that spectrum of certainty, from no certainty whatsoever to well-established fact. This turned out to be a great lens to look at ideas like global warming and evolution. But all of this was pretty hypothetical. My friend described the spectrum in fairly vague terms, and students were only to consider how certain they were of particular measurements or ideas.

A few years ago, I stumbled upon a blog post that reminded me of this. A blogger was taking ideas like string theory, and placing them along a very well defined spectrum of certainty along a number line that he had created. Unfortunately, a half hour of searching has turned up nothing, and so now I’m thinking of recreating this myself.

So this is where I’d like to turn to you for help. Some questions to think about if you were trying to describe the spectrum of certainty.

1. What are the various classifications along this range (completely uncertain, somewhat uncertain, well established…). I’d like to avoid putting in a category for well established fact, and instead think of a way of describing those things are well accepted from the point of having a very small uncertainty.
2. What ideas would you place on this spectrum? Where would they go?
3. What about measurement uncertainty? Could you match up various percent uncertainties with different categories (that would seem to be not idea). How should the spectrum of certainty apply to measured and calculated quantities?

Ultimately, I’d like to turn this into some sort of poster for the front of the room, so please send me your ideas.

1. August 27, 2012 8:14 am

In fact that last sentence might, for a 10th grader, fall far, far to the right on the spectrum of certainty, but for my 12th graders, it will (eventually, hopefully) fall way off to the left (since it implies an instantaneous propagation of the interaction). But then this is totally weird… we use Newton’s Universal Law of Gravitation very successfully to do all kinds of amazing things. I’m overcomplicating this, aren’t I?

2. August 27, 2012 9:42 am

What do you mean by certainty? Like the various approaches to the meaning of probability, different approaches to certainty could result in different continua.

August 27, 2012 10:11 am

This might be the original blog post you were thinking of:
http://scienceblogs.com/startswithabang/2010/07/21/how-good-is-your-theory/

• August 27, 2012 10:14 am

Yes, oh my god yes! I’m embarrassed to say how many times I was doing site searches of starts with a bang and couldn’t turn this up. Thanks so much!

4. August 27, 2012 11:42 am

Thanks for the heads up John and BuffyThePhysicist. A concept worth spreading. I will share with others – educators, parents, students.

5. August 27, 2012 3:29 pm

After reading the “How Good is Your Theory” article plus comments, I felt that Brian (look down the list of comments) brings up a point. I have seen this point argued within the field of Evolution Theory. I find the points relevant when defining degrees of certainty. Brian says:
“Scientific laws are not well confirmed theories. Evolution is as well confirmed as you’d like, but it will never become the law of evolution because it is much broader than a law. Likewise physical laws, such as laws of thermodynamics. They are not well confirmed theories. A theory such as quantum mechanics or relativity will have to explain these laws, but that shows that laws are not theories, but regular phenomena.”

• August 27, 2012 4:03 pm

You’re totally right. I didn’t see that in my first pass, and need to modify the most confirmed end to reflect that. Well accepted? Comprehensive theory? Not sure what works well there.

• August 27, 2012 10:30 pm

What timing! Just kicking back to relax this evening and scrolling through my news feed and what comes across? A link to an article on The National Academies web site on the subject of the definition of scientific “theory”: http://www.nationalacademies.org/evolution/TheoryOrFact.html . I’m too tired to carefully think through what terminology or visual tool would work best but I do really like the idea of teaching kids… or anybody… to carefully consider the quality of the study design and resulting data, strength of the results, and breadth of support from independent, unbiased sources on their level certainty.

6. August 27, 2012 5:56 pm

I kind of like a quote from my book, one of the better ones, if I do say so: “A good general knows that the impossible is probably just improbable”. Think I will tweet that out!

7. August 27, 2012 7:04 pm

Cool post! I used to think that all pure math fit into the “scientific law” category (as certain as possible), but then I came across the Axiom of Choice–a mathematical concept which may or may not be true!! That would definitely be an interesting thing to try and place on the spectrum.

• August 30, 2012 5:08 pm

I don’t understand how an axiom “may or may not be true”. It is true in mathematical systems that include it.
Perhaps you meant that it is consistent with axiom systems that are used to define the real numbers, but that one can get a powerful system with many of the properties we’re interested in even without this axiom.
Axioms are not on the “certainty” scale—they are assumptions that you make in order to build an interesting system. Within that system, they are absolutely certain—outside that system they are not even meaningful statements.

A scientific law is a concise summary of empirical observations—very much lower on the certainty scale than a mathematical proof.

• August 30, 2012 6:18 pm

Ah, you’re right, I think I see my mistake. I think that they way my professor introduced me to the Axiom of Choice was that he suggested that it was initially thought to have logically followed from the basic axioms of number theory (much like the parallel lines postulate was initially believed to follow from Euclid’s other geometry axioms). However, it is still possible that the Axiom of Choice (named so because it is believed to be independent, as you explained axioms are) is true or false because it is still theoretically possible to prove or disprove the axiom from the other axioms in number theory–hence the uncertainty.

Unlike the the parallel lines postulate, I do not think the axiom of choice has been proven to be logically independent of the other number theory axioms, but I could be very wrong–it has been a long time since I took those courses. 🙂

• August 30, 2012 10:14 pm

I quote from Wikipedia’s “Axiom of Choice” page:

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model (the constructible universe) which satisfies ZFC and thus showing that ZFC is consistent. Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF¬C (ZF with the negation of AC added as axiom) and thus showing that ZF¬C is consistent. Together these results establish that the axiom of choice is logically independent of ZF. The assumption that ZF is consistent is harmless because adding another axiom to an already inconsistent system cannot make the situation worse. Because of independence, the decision whether to use of the axiom of choice (or its negation) in a proof cannot be made by appeal to other axioms of set theory. The decision must be made on other grounds.

• August 30, 2012 10:32 pm

I suppose we can’t rule out that what someone wishes as an axiom is so malformed as to be self-contradictory.