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Since the sun going nova is not a random event, strict frequentists deny that there is a probability to associate with it.
Among candidate stars for going nova I would think you could treat it as a random event. But Sol is not a candidate and so doesn't even make it into the sample set. So it's a very badly constructed setup. It's like looking for a needle in 200 million haystacks but restricting yourself only to those haystacks you already know it cannot be in. Or do I have that wrong.
I don't think one would simply ignore the dice, and what data is the frequentist drawing upon in the comic which specifies the null?
How about "the probability of our sun going nova is zero and 36 times zero is still zero"?
Although... continuing with the XKCD theme if you divide by zero perhaps that would increase the odds. ;)
In response to
XKCD - Frequentist vs. Bayesians
No, it's not fair. Given the setup, the null hypothesis would be, I think, 'neither the Sun has exploded nor the dice come up 6', and so when the detector goes off we reject the 'neither x nor y' in favor of 'x or y' - and I think the Bayesian would agree too that 'either the Sun has exploded or the dice came up 6'!
I think the null hypothesis is "the neutrino detector is lying" because the question we are most interested in is if it is correctly telling us the sun has gone nova. If H0 is the null hypothesis and u1 is the chance of a neutrino event and u2 is the odds of double sixes then H0 = µ1 - µ2. Since the odds of two die coming up sixes is vastly larger than the odds of the sun going nova in our lifetime the test is not fair.
In response to
On counting and addition
Clear writing, clear thinking, much appreciated.
An aside: the Venus fly trap plant has fibers in its hinged petals. Touching one will not close it. Touching more than one with a delay between touches will not close it. Touching one or more fibers in succession will close it. This plant moves as if it can count and is aware of time. Learning that caused me to re-think what it means to count, as did your essay. Except the plant-fact is interesting while your essay is useful.
Plants do not count and have no awareness of time or of anything at all. The exact method by which venus fly traps activate is unknown but it seems hard to me to attribute it with the ability to count. That kind of teleological explanation is something we are cognitively biased to give but it fails to be explanatory.
Sunflowers do not turn their heads to face the sun because they want to catch more sunlight. They turn towards light because those cells that are in shadow receive more auxin which in turn stimulates the elongation of the cell walls causing the plant to grow in the opposite direction and towards the light. Natural selection will tend to favor those individuals that can gather more light than those which do not. There is no teleology involved.
In response to
On counting and addition
I generally agree with point (1) but the point is irrelevant. Counting isn't what makes 2 + 2 = 4 true. Although that is how we all learn to do math, by counting and memorizing addition and multiplication tables. I owe it all to my 3rd grade teacher. ;)
On point (2): "on our macro scale of reality, on the scale of things we perceive with our senses, discrete, separate objects are a feature of the map, not the territory; they exist in your mind, not the reality. In the reality, there's just a lot of atoms everywhere"
There are no atoms at the macro scale. Or, if you like, atoms are everywhere. A chair is an "atom" of my dinning room furniture set and I can choose to count 5 items, four chairs and a table, or one item, one dinning room set. How I choose to cut up the world will determine which answer I get. But I am very confident that rocks and trees and universities and constitutions do not exist in my mind. They have an objective ontology that is independent of my personal subjective needs, interests and desires. Which is what it means for something to be real.
"Was 2+2=4 before humans were around to invent that equation?"
The statement: "2 + 2 = 4" is absolutely true because it is true in all possible worlds. Humans did not invent the equation, we invented the symbols and means of expressing it but the relation that is expressed in the words is an objective feature of the world that is true regardless of our opinions about it. Scientific facts have the world to word direction of fit. That is, they are true only to the extent they correspond to the world.
"we can certainly speak of single photons"
Only if we choose to observe them as particles. Photons have been observed experimentally to be both particles and waves. "The measurement apparatus detected strong nonlocality, which certified that the photon behaved simultaneously as a wave and a particle in our experiment. This represents a strong refutation of models in which the photon is either a wave or a particle." This presents a significant challenge to certain theories.
To clarify (I didn't do a good job above), I meant to ask "do certain perceived psychological effects (which probably do correlate with neurophysiological mechanisms) correlate with voting events AND significant positive and negative effects on the populace in terms of perceived well-being and productivity?
I did not know that about banking, although I did not expressly believe the alternative either. I will definitely look at that a little more. Intuitively I also agree with the sentiment that many other seemingly mundane things probably have a greater overall impact on societal production than relatively uncommon events.
Ok, I do wonder how one would distinguish between perceived effects vs real effects. The real effects of say civil rights legislation was greater freedom and opportunity for minorities. We are a better more productive society when we, at least in theory, give everyone an equal chance to succeed. That's the real material result of the 60's civil rights movement.
The psychological effect of those who benefited was maybe "I am a valued member of society." I'm not sure how one teases that apart from the positive effect of simply being able to get a job or a loan without being discriminated against. I am just wondering out loud. I really wonder how much of a difference perception or attitude makes over and above real material changes.
I suspect that my perceptions positive or negative of the results on an election are determined by whether or not I experience real benefit or harm. I also suspect that we sort of backtrack and revise our memories to convince ourselves that we are masters of our domain when the opposite may be true.
But I don't know. I could be all wrong.
In response to
Does My Vote Matter?
I wonder if the psychological effects of voting on individuals (feelings of empowerment, possibly of hopelessness or hope) have a significant positive or negative effect on the populace in terms of productivity or well-being soon before and/or shortly after an election.
And if so, how the magnitude of such an effect might correlate with the scale, expected outcome, or actual outcome of a given election (or issue). i.e. might people feel more empowered
(a) After voting in a Presidential election where their votes have a smaller effect on the outcome, but where the result affects more people in a larger way, or
(b) After voting in a local county election where their vote has a larger effect on the outcome, but where the result of the election affects fewer people in a smaller way, or
(c) According to some reliable function relating scale and impact of election
If the confidence fairy has been shown not to exist. (The confidence fairy is the theory that the reason banks are not lending right now is due to a lack of confidence in the market.) Then why should we believe that feelings of hopelessness or empowerment will effect the economy? (productivity is an economic feature) What seems to me more likely to affect productivity is whether or not one got a good night's sleep the night before and ate a decent breakfast.
If folk psychology (hope, despair) is epiphenominal then there is no reason to believe they have causal effects in the world.
In response to
Does My Vote Matter?
This is the wrong way to think about it. One's vote matters not because in rare circumstances it might be decisive in selecting a winner. One's vote matters because by voting you reaffirm the collective intentionality that voting is how we settle our differences. All states exist only through the consent of it's people. By voting you are asserting your consent to the process and it's results. Democracy is strengthened through the participation of the members of society. If people fail to participate society itself suffers.
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You're getting old. The long term prognosis is that the condition is fatal. ;)