Consider first the two possible outcomes conditional on today being Monday. Since Sleeping Beauty always is awakened on Monday regardless of the coin toss result, P(Monday-Heads) = P(Monday-Tails). Consider next the two possible outcomes conditional on the coin having landed tails. Since in that case Sleeping Beauty is awakened once on Monday and once on Tuesday, P(Monday-Tails) = P(Tuesday-Tails), which is something that the Thirders, Halfers and Double-halfers all agree on. We therefore have that P(Monday-Heads) = P(Monday-Tails) = P(Tuesday-Tails). Lastly, since Sleeping Beauty isn't inquiring about the probabilities that any of those three outcomes will occur at least once during her current experimental run, but rather about the probability that her current awakening episode is the realization of one of those three outcomes, the three possibilities are exclusive and exhaustive, and their probabilities must therefore sum up to 1. They therefore all three are 1/3, and P(Tails) = P(Monday-Tails) + P(Tuesday-Tails) = 2/3. — Pierre-Normand

whenever she awakens, the coin landed (or will land) tails two times out of three — Pierre-Normand

However, it seems ridiculous to say that an iterative string creation program is somehow equivalent to its outputs. No one will be happy if they hire a software engineer to create a specific program and they receive an iterative string generator that would, eventually, produce the ideal program they are looking for. — Count Timothy von Icarus

Evolving the universe forward might allow you to turn T1 into any other time in the universe, but in order to halt the process and output the description of the time you want to describe using T1 you'd need to already have a total description of the time you want so that you can match the two. — Count Timothy von Icarus

Anyhow, I found simple requests to "critically assess" my answers can mitigate the agreeability bias. — Baden

hypostatization (reification) — NOS4A2

The thirder view is that only the current slice that you might be is relevant, and there are more being-interviewed slices in the tails partition, so you're more likely one of those. — Srap Tasmaner

the correct analysis is that the coin flip partitions SB's future slices into a heads set and a tails set, just two, equal chances of being in each set. — Srap Tasmaner

She is therefore being asked "What is P(C | M) , where M is your current mental state?" — sime

Task :

Determine the marginal distribution P (C = head ) from the above premises — sime

It's just right, look at the code!

All coding something up does is let you check a calculation for it being correct, not whether it's the appropriate calculation to do. — fdrake

The traditional use of pronouns is to identify sex, not gender. — Philosophim

import numpy as np
import matplotlib.pyplot as plt

def experiment(trials):
    headsProbability = 0.0
    for heads in range(trials + 1):
        headArrangements = np.math.factorial(trials)/np.math.factorial(trials-heads)/np.math.factorial(heads)
        headsRightAnswer = heads / (heads + (trials - heads)*2.0)
        headsProbability += headArrangements / np.power(2.0, trials) * headsRightAnswer
    return headsProbability

trials = [i+1 for i in range(50)]
results = [experiment(t) for t in trials]

plt.plot(trials, results, '-')
plt.ylabel("heads probability")
plt.xlabel("trials")
plt.show()

((This is, I don't know, maybe the third time I've argued with Michael about something and then concluded he was right all along.)) — Srap Tasmaner

In our version, the base rate of heads interviews is 1 in 3. Make it 1 in 1000. (That is, 999 awakenings on tails, not 2.) Isn't it obvious that if I'm a subject in such an experiment, I know it's far more likely I'm being asked for my credence because my coin came up tails? If I'm one of 1200 subjects, I know there are 600,000 interviews, only 600 of which were for heads, while 599,400 were for tails. Equally likely that this interview is for heads as for tails? Not by a long shot. — Srap Tasmaner

Let's say that I wanted to bet on a coin toss. I bet £100 that it will be tails. To increase the odds that it's tails, I ask you to put me to sleep, wake me up, put me back to sleep, wake me up, put me back to sleep, wake me up, and so on. Does that make any sense? — Michael

She can't. — L'éléphant

The probability that the coin will land heads and she will be woken on Monday is 1/2.
The probability that the coin will land tails and she will be woken on Monday is 1/2.
The probability that the coin will land tails and she will be woken on Tuesday is 1/2. — Michael

Bet on heads or tails. If tails, you get to repeat the same bet again, on the same toss — hypericin

This version looks a lot clearer to me, and the question at the end looks like a deception. 2 possible worlds, contain 3 possible identities. So other things (ie coins) being equal, I am more likely to be one of two than one of one. So P. (only child) is 1/3 notwithstanding P. (heads) is 1/2, because tails is twice as fruitful as heads. — unenlightened

since he gains no new relevant evidence if he wakes up during the experiment. — Michael

To emphasize this answer, imagine head: they wake her the once, but tails, they do it 100 times before the experiment ends. The coin flip odds are still 50/50, but the odds that on a random waking she sees tails is overwhelming. — noAxioms

That was my whole argument regarding all those "crowning achievement" superlatives early in the thread. I wasn't putting humans down; merely pointing out that better or worse depend entirely on the criteria of comparison. — Vera Mont

Human beings whilst in one regard are capable of performing completely selfless acts of kindness are equally capable of doing the opposite to such extremes as murder and endless wars. — invicta

The upshot of all this is that it is pretty much impossible to set out the structure of the ontological argument in first-order logic. Or if you prefer, that the argument does not make sense.

Hence it is not valid. — Banno

. But in the non-organic realm, what sense does it make to speak of information at all? — Wayfarer

My guess is that it comes down to the ability to discern between small differences. This is also what instruments do for humans and computers, allow for greater discernablity. — Count Timothy von Icarus

Here is a demonstration — Count Timothy von Icarus

• Every painting ever painted
• Every painting, with the subjects replaced by anthropomorphic versions of every animal, in every permutation
• Every one of your pages, rendered in every font
• The above, where every character is rendered in every permutation of fonts
• The above, but where every character is also rendered in permutations of every discernable shade
• The above, but where every permutation is rotated from 0 to 360 degrees, to the limits of discernibility
• Every visual experience ever had by every human, awake, asleep, drugged
• And every other animal
• The above, but where the scene is rotated in every discernable degree around all 3 axes
• The above, but where overlaid on top is each and every one of the page images above, with every discernable permutation of transparency, scale, offset
• Every distinct vantage point of every location on earth, at every scale, and every time
• ...and every other planet, and every other visually distinct location in the universe
• ...then overlay the pages
• ...overlaid on top of that, variations where every forum member here is mooning the "camera", at every discernable location, scale, posture, age, skin tone...

If algorithms are just names, a relatively bare bones symbol shuffling algorithm is almost godlike in it's ability to name almost everything. — Count Timothy von Icarus

It is actually incredibly difficult to define "computer" in such a way that just our digital and mechanical computers, or things like brains, are computers, but the Earth's atmosphere or a quasar is not,without appealing to subjective semantic meaning or arbitrary criteria not grounded in the physics of those systems. — Count Timothy von Icarus

The mistake I mean to point out is that we generally take 10÷2 to be the same thing as 5. Even adamant mathematical Platonists seem to be nominalists about computation. An algorithm that specifies a given object, say a number, "is just a name for that number." — Count Timothy von Icarus

If the state of a computer C2 follows from a prior state C1, what do we call the process by which C1 becomes C2? Computation. Abstractly, this is also what we call the process of turning something like 10 ÷ 2 into 5.

What do we call the phenomena where by a physical system in state S1 becomes S2 due to physical interactions defined by the laws of physics and their entailments? Causation. — Count Timothy von Icarus

• There is no such thing as causation that goes wrong. It does what it does, it is infallible by its nature. Whereas at every step, the possibility of error hovers over computation.
• Causal processes don't inherently require continuous energy input. Strike the cue ball, and the billiards will take care of themselves. Whereas in a computational process, to proceed requires energy at every step. Cut the power, occlude the cerebral artery, and the computation comes to a screeching halt.
• There is no notion of accuracy of causal systems. They are in themselves infinitely accurate. Whereas for many computations, to achieve perfect accuracy requires infinite time and energy.
• Causation is something that stuff does. Whereas computation, however sophisticated, can never achieve stuffhood. You can computationally simulate every feature of a waterfall, down to the most minute detail. But no matter how sophisticated, you can never touch a waterfall simulator and get your fingers wet.

In many respects, it is impossible to distinguish communication from computation in contemporary theories. I think they are different and that this shows a weakness in the theories. — Count Timothy von Icarus