A

B

Observation
Induction
No assumption, no hypothesis
Empirical stance / method
Repeated observation of presence or absence, occurence or
nonoccurence of the event is key, i.e. prediction is an inference with a probability of error
Power of a series of observations is dependent on (a) the degree to
which the event is observable, as well as (b) the number of observations
Relevant to BottomUp information processing Frequentist, Bayesian

Reasoning, calculation
Deduction
An absolute numerical probability is at hand
Rationalistic stance / method
Prediction is is based on a mathematical operation, ie. an extension
of logic
Prediction is binomial i.e. absolute and either true or false.

In the A condition, probability of error is dependent on the
frequency distribution in the set of repeated observations, which varies with
every “bit” of new information / observation—Yes or No, True or False,
Occurence or Nonoccurence. The prediction that is based on the initial bit of
information carries the highest probability of error, decreasing as
observations accumulate.
In the B condition, i.e. when the probability that an event
takes place or that a proposition is true is a given, predictions are based on,
and only on, this constant value of probability.
Inference based on observation cannot be justified in the B
condition, for the probability is constant, rendering observational evidence
redundant.
The Beads Task is designed as a measure of the tendency on the
part of the observersubject to jump to conclusions. I find it hard to understand—literally: Although
the subjects are informed at the outset regarding the constant figure of
probability for True or False, they are offered a series of repeated
observations until they feel confident to make a guess, a forced choice between
True and False.
M: Number of beads that are in the majority
m: Number of beads that are in the minority
B: Total number of beads in each of the two jars = M+m
D: Draw
n: Number of draws (observations)
Pr: Probability of a correct guess regarding the jar of
origin for the bead presented = Ratio of the number of beads in the Majority to
the Total number of beads in each jar
Pw: Probability of an incorrect guess regarding the jar of origin
for the bead presented = Ratio of the number of beads in the Minority to the
Total number of beads in each jar
The initial observation is the only basis for the forced
choice, and this is independent from the ratio of M/n.
Induction, based on probability of error (Pw) is redundant,
because:
Pw= (m/B)ⁿ for any number of draws (observations)
Pr= M/B at the initial draw (observation)
M, m, n and B are positive integers.
If m is smaller than M, then M/m is bigger than 1.
Pw will decrease at every draw, to reach 0 when the draw number is ∞.
If m is smaller than M, then M/m is bigger than 1.
Pw will decrease at every draw, to reach 0 when the draw number is ∞.
For no value of n will Pw be bigger than M/B, i.e. the Pr at
the initial draw.
Hence my question:
What is the question of the Beads Task?
How quickly does the subject jump to the conclusion? (1), or
How long does it take the subject to figure out the
redundancy of observation following the initial draw? (2)
If (1), is it that the task takes advantage of a trick that
involves misguiding the subject? (3)
If (3), how is this really relevant to psychotic thought
disorder?
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