Dec 17, 2024 10:24 PM
(This post was last modified: Dec 17, 2024 10:28 PM by Magical Realist.)
A good and somewhat challenging article on the notion of probability being an objective and subjectively-independent aspect of reality. I have always suspected probabilities of being mathematical fictions dependent on the degree of our knowledge and experience. Hume would probably have something to say about this were he alive today. Are future events really somehow mystically constrained by what has happened in the past? Or is that just how we have become accustomed to our own experience of the events of our lives?
https://www.nature.com/articles/d41586-0...0objective.
"Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past, or is happening now outside our immediate experience. Uncertainty has been called the ‘conscious awareness of ignorance’1 — be it of the weather tomorrow, the next Premier League champions, the climate in 2100 or the identity of our ancient ancestors.
In daily life, we generally express uncertainty in words, saying an event “could”, “might” or “is likely to” happen (or have happened). But uncertain words can be treacherous. When, in 1961, the newly elected US president John F. Kennedy was informed about a CIA-sponsored plan to invade communist Cuba, he commissioned an appraisal from his military top brass. They concluded that the mission had a 30% chance of success — that is, a 70% chance of failure. In the report that reached the president, this was rendered as “a fair chance”. The Bay of Pigs invasion went ahead, and was a fiasco. There are now established scales for converting words of uncertainty into rough numbers. Anyone in the UK intelligence community using the term ‘likely’, for example, should mean a chance of between 55% and 75% (see go.nature.com/3vhu5zc).
Attempts to put numbers on chance and uncertainty take us into the mathematical realm of probability, which today is used confidently in any number of fields. Open any science journal, for example, and you’ll find papers liberally sprinkled with P values, confidence intervals and possibly Bayesian posterior distributions, all of which are dependent on probability.
And yet, any numerical probability, I will argue — whether in a scientific paper, as part of weather forecasts, predicting the outcome of a sports competition or quantifying a health risk — is not an objective property of the world, but a construction based on personal or collective judgements and (often doubtful) assumptions. Furthermore, in most circumstances, it is not even estimating some underlying ‘true’ quantity. Probability, indeed, can only rarely be said to ‘exist’ at all.
Chance interloper
Probability was a relative latecomer to mathematics. Although people had been gambling with astragali (knucklebones) and dice for millennia, it was not until the French mathematicians Blaise Pascal and Pierre de Fermat started corresponding in the 1650s that any rigorous analysis was made of ‘chance’ events. Like the release from a pent-up dam, probability has since flooded fields as diverse as finance, astronomy and law — not to mention gambling.
To get a handle on probability’s slipperiness, consider how the concept is used in modern weather forecasts. Meteorologists make predictions of temperature, wind speed and quantity of rain, and often also the probability of rain — say 70% for a given time and place. The first three can be compared with their ‘true’ values; you can go out and measure them. But there is no ‘true’ probability to compare the last with the forecaster’s assessment. There is no ‘probability-ometer’. It either rains or it doesn’t.
What’s more, as emphasized by the philosopher Ian Hacking2, probability is “Janus-faced”: it handles both chance and ignorance. Imagine I flip a coin, and ask you the probability that it will come up heads. You happily say “50–50”, or “half”, or some other variant. I then flip the coin, take a quick peek, but cover it up, and ask: what’s your probability it’s heads now?
Note that I say “your” probability, not “the” probability. Most people are now hesitant to give an answer, before grudgingly repeating “50–50”. But the event has now happened, and there is no randomness left — just your ignorance. The situation has flipped from ‘aleatory’ uncertainty, about the future we cannot know, to ‘epistemic’ uncertainty, about what we currently do not know. Numerical probability is used for both these situations.
There is another lesson in here. Even if there is a statistical model for what should happen, this is always based on subjective assumptions — in the case of a coin flip, that there are two equally likely outcomes. To demonstrate this to audiences, I sometimes use a two-headed coin, showing that even their initial opinion of “50–50” was based on trusting me. This can be rash."
https://www.nature.com/articles/d41586-0...0objective.
"Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past, or is happening now outside our immediate experience. Uncertainty has been called the ‘conscious awareness of ignorance’1 — be it of the weather tomorrow, the next Premier League champions, the climate in 2100 or the identity of our ancient ancestors.
In daily life, we generally express uncertainty in words, saying an event “could”, “might” or “is likely to” happen (or have happened). But uncertain words can be treacherous. When, in 1961, the newly elected US president John F. Kennedy was informed about a CIA-sponsored plan to invade communist Cuba, he commissioned an appraisal from his military top brass. They concluded that the mission had a 30% chance of success — that is, a 70% chance of failure. In the report that reached the president, this was rendered as “a fair chance”. The Bay of Pigs invasion went ahead, and was a fiasco. There are now established scales for converting words of uncertainty into rough numbers. Anyone in the UK intelligence community using the term ‘likely’, for example, should mean a chance of between 55% and 75% (see go.nature.com/3vhu5zc).
Attempts to put numbers on chance and uncertainty take us into the mathematical realm of probability, which today is used confidently in any number of fields. Open any science journal, for example, and you’ll find papers liberally sprinkled with P values, confidence intervals and possibly Bayesian posterior distributions, all of which are dependent on probability.
And yet, any numerical probability, I will argue — whether in a scientific paper, as part of weather forecasts, predicting the outcome of a sports competition or quantifying a health risk — is not an objective property of the world, but a construction based on personal or collective judgements and (often doubtful) assumptions. Furthermore, in most circumstances, it is not even estimating some underlying ‘true’ quantity. Probability, indeed, can only rarely be said to ‘exist’ at all.
Chance interloper
Probability was a relative latecomer to mathematics. Although people had been gambling with astragali (knucklebones) and dice for millennia, it was not until the French mathematicians Blaise Pascal and Pierre de Fermat started corresponding in the 1650s that any rigorous analysis was made of ‘chance’ events. Like the release from a pent-up dam, probability has since flooded fields as diverse as finance, astronomy and law — not to mention gambling.
To get a handle on probability’s slipperiness, consider how the concept is used in modern weather forecasts. Meteorologists make predictions of temperature, wind speed and quantity of rain, and often also the probability of rain — say 70% for a given time and place. The first three can be compared with their ‘true’ values; you can go out and measure them. But there is no ‘true’ probability to compare the last with the forecaster’s assessment. There is no ‘probability-ometer’. It either rains or it doesn’t.
What’s more, as emphasized by the philosopher Ian Hacking2, probability is “Janus-faced”: it handles both chance and ignorance. Imagine I flip a coin, and ask you the probability that it will come up heads. You happily say “50–50”, or “half”, or some other variant. I then flip the coin, take a quick peek, but cover it up, and ask: what’s your probability it’s heads now?
Note that I say “your” probability, not “the” probability. Most people are now hesitant to give an answer, before grudgingly repeating “50–50”. But the event has now happened, and there is no randomness left — just your ignorance. The situation has flipped from ‘aleatory’ uncertainty, about the future we cannot know, to ‘epistemic’ uncertainty, about what we currently do not know. Numerical probability is used for both these situations.
There is another lesson in here. Even if there is a statistical model for what should happen, this is always based on subjective assumptions — in the case of a coin flip, that there are two equally likely outcomes. To demonstrate this to audiences, I sometimes use a two-headed coin, showing that even their initial opinion of “50–50” was based on trusting me. This can be rash."
