Conflicting Ideas of Probability & Likelihood in the Wikipedia article on Monopoles

In the Public Encyclopedia’s (present) discussion of the hypothetical existence of a magnetic monopole

in nature, among the possible fundamental particles, exemplifies both (and maybe >2) “sides” in the debate over what probability means:

Magnetism in bar magnets and electromagnets does not arise from magnetic monopoles, and in fact there is no conclusive experimental evidence that magnetic monopoles exist at all in the universe.

Since Dirac’s 1931 paper[8] , several systematic monopole searches have been performed. Experiments in 1975[10] and 1982[11] produced candidate events that were initially interpreted as monopoles, but are now regarded as inconclusive.[12]Therefore, it remains an open question whether or not monopoles exist.

Further advances in theoretical particle physics, particularly developments in grand unified theories and quantum gravity, have led to more compelling arguments[which?] that monopoles do exist. Joseph Polchinski, a string-theorist, described the existence of monopoles as “one of the safest bets that one can make about physics not yet seen”.[13]These theories are not necessarily inconsistent with the experimental evidence. In some theoretical models, magnetic monopoles are unlikely to be observed, because they are too massive[why?] to be created in particle accelerators, and also too rare in the Universe to enter a particle detector with much probability.[13] (According to these models, there may be as few as one monopole in the entire visible universe.[14])

Here are a few potential explanations of how one is to arrive at a probability number:

  • opinion — it’s just Joseph Polchinski’s opinion
  • frequentism — Europeans never observed a black swan before exploring the New World, therefore black swans have 0% chance of existing.
  • frequentism + how hard you’ve searched — the probability comes attached with a confidence number. If you’ve stayed within the city limits of Minneapolis your entire life, you should attach a low confidence to your search for tarantulas the size of your head. But we’ve tried very hard to find monopoles, and haven’t. So a “more confident” zero on that one.
  • Dutch Books — could we arbitrage Joseph Polchinski’s “sure thing” bet?
  • authority, credibility, expertise — who exactly is this Joseph Polchinski character, anyway? And who says he’s such an expert? Is he an interested party? I don’t believe what vested interests and biased sources say, even if it happens to be true.
  • propensity — good gravy, I don’t even get to invoke the famous “coin has an innate propensity to tend to certain heads/tails ratio” because it would get us nowhere in terms of “Do monopoles have a propensity to exist or not?”. Anyway propensity merely passes the buck even in the cases where it does make sense.
  • reason & facts — there is no conclusive evidence that monopoles exist, yet they haven’t been proven impossible. I will withhold my opinion and it would be unreasonable to assign a probability mass to either alternative. We’re simply somewhere ∈ [0%, 100%] at this time.
  • model strength — some of these models sound suspect. It’s constructed “just so” that there’s only one monopole in the universe? Very convenient for you, when you want to say monopoles exist and we just haven’t seen them yet. Pull the other one!

All of the stochastic maths is done with the Kolmogorov axioms, i.e. it’s done with measure spaces with a fixed | finite | constant measure (= 100% of the probability mass) without connecting that to “how likely” a one-off event is. (Much like some maths you could pass off as financial modelling “is just” the theory of martingales = fair repeated bets.) But it needn’t have be called “likelihood”, it could have been “fuzzy truthiness” or “believability” or “motions of a fixed-volume-but-infinitely-divisible liquid”. As Cosma Shalizi puts it here:

Probabilities are numbers that tell us how often things happen.

Mathematicians are anxious to get on with talking about ergodicity, Markov transition matrices, and large-deviations theory. What you’re seeing in this block quote is the handoff between mathematicians and philosophers—essentially the mathmos say “You take it from here to the firm foundation” and philosophers, so far, haven’t been able to.


Is there a problem in practice due to not having a sound foundation on our concept of probability? Yes. It’s not secure to move forward with the rear flank uncovered. The lax attitude toward probability and “We’ll do the best with what we can” lets us make up numbers for the {pessimistic, neutral, optimistic} scenarios of our forecasting spreadsheets.

Think about when some consequential decision by a powerful group depends on the value of one parameter. It could be

  • the likelihood of Floridian home prices decreasing by more than 5% in a year,
  • the likelihood of [foreign country X] attacking “us” in response to Y,
  • the likelihood of RHIC creating a strangelet and swallowing the world in a minisecond,
  • the likelihood of construction on the new power plant going over budget,
  • the likelihood of borrowing rates staying this low for another 5 years,
  • the likelihood of real GDP rising at least 2%/year during the next 10 years,
  • the likelihood of our borrowing rate quadrupling
  • the likelihood that your college degree will “be worth it” to you
  • the likelihood of this whole startup thing actually working.

and I get to either rely on

  • historical data (“home prices have always gone up before”, “we haven’t seen any problems with financial derivatives yet”, “correlation with a Gaussian copula has always worked so far”),
  • reason and facts (and multiply an endless debate among the experts),
  • or gut (throw in some numbers that sound pessimistic, optimistic, and neutral, and we’ll see how the forecast behaves).

We got nuthin’.

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