Speed-Accuracy Trade-Offs (in Physical Cognition)

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Speed-Accuracy Trade-Offs (in Physical Cognition)

s.butterfill@warwick.ac.uk & c.sinigaglia

Ask now, come back to this later

McCloskey, Caramazza, & Green (1980, p. figure 2B)

McCloskey et al. (1980, p. figure 2D)

No one has every observed such a trajectory. So it cannot be on the basis of what they have actually observed that they make this prediction.

why?

because fast processes make it appear so
(Kozhevnikov & Hegarty, 2001)

## 1. Perceiving Impetus

background: representational momentum

Sometimes when adult humans observe a moving object that disappears, they will misremember the location of its disappearance in way that reflects its momentum; this effect is called _representational momentum_ (Freyd & Finke, 1984; Hubbard, 2010).

The trajectories implied by representational momentum reveal that the effect reflects impetus mechanics rather than Newtonian principles (Freyd & Jones, 1994; Kozhevnikov & Hegarty, 2001; Hubbard, Blessum, & Ruppel, 2001; Hubbard, 2013). And these trajectories are independent of subjects' scientific knowledge (Freyd & Jones, 1994; Kozhevnikov & Hegarty, 2001). Representational momentum therefore reflects judgement-independent expectations about objects’ movements which track momentum in accordance with a principle of impetus.% \footnote{ Note that momentum is only one of several factors which may influence mistakes about the location at which a moving object disappears (Hubbard, 2005, p. \ 842). %> : %> %> `The empirical evidence is clear that (1) displacement does not always correspond to predictions based on physical principles and (2) variables unrelated to physical principles (e.g., the presence of landmarks, target identity, or expectations regarding a change in target direction) can influence displacement.' %> %> ... %> %> `information based on a naive understanding of physical principles or on subjective consequences of physical principles appears to be just one of many types of information that could potentially contribute to the displacement of any given target' %> }

Hubbard 2005, figure 1a; redrawn from Freyd and Finke 1984, figure 1

Hubbard 2005, figure 1b; drawn from Freyd and Finke 1984, table 1

**Representational momentum suggests that there are fast processes which predict the future trajectories of physical objects.**

There are fast process in you
which predict
the future trajectories of physical objects

and they influence perceptual experience.

Next question:

What principles underpin these predictions?

Kozhevnikov & Hegarty (2001, figure 1)

Fix shape and density.

How would increasing the object’s size affect how quickly it decelerates when launched vertically?

Impetus prediction: larger size entails greater deceleration (so slower ascent).

Newtonian prediction: larger size entails lower deceleration (so faster ascent) if considering air resistance; otherwise size makes no difference.

Fix shape and density. How would increasing the object’s size affect how quickly it decelerates when launched vertically? Impetus: larger size entails greater deceleration (so slower ascent). Newtonian: larger size entails lower deceleration (so faster ascent) if considering air resistance; otherwise size makes no difference.

simplified from Kozhevnikov & Hegarty (2001)

But even more convincingly, the prediction generated by Kozhevnikov and Heggarty’s conjecture about the computational description of the system underpinning representational momentum has been directly confirmed.

So while not decisive, I take this to be strong evidence for a **vertical distinction** between two systems for physical cognition.

McCloskey et al. (1980, p. figure 2D)

why?

because fast processes make it appear so
(Kozhevnikov & Hegarty, 2001)

significance

connecting fast and slow processes

Two points of significance. 1. fast processes influence slow judgements via phenomenal modifications. 2. speed-accuracy trade-offs

How do fast processes influence slow processes?

ex: explicit verbal judgements

fast process ~ representational momentum

-> phenomenology of experience

-> thinking about experience ~ slow process

-> explicit verbal judgement

phenomenology connects fast and slow indirectly
, leaving room for discretion.

We do not need to assume that this is a matter of inference, nor of representational contents being transformed.

It’s up to you whether to make the connection (experts reject it, novices do not).

significance

speed vs accuracy trade-off

Any broadly computational process faces a trade-off between speed and accuracy ...

How can you trade away accuracy to gain speed?

They were led to a conjecture about the computational description by reflection on the fact that **any broadly inferrential process must make a trade-off between speed and accuracy**.

‘To extrapolate objects’ motion on the basis of [e.g. Newtonian] physical principles, one should have assessed and evaluated the presence and magnitude of such imperceptible forces as friction and air resistance ... This would require a time-consuming analysis that is not always possible.

‘In order to have a survival advantage, the process of extrapolation should be fast and effortless, without much conscious deliberation.

‘Impetus theory allows us to extrapolate objects’ motion quickly and without large demands on attentional resources.’

Kozhevnikov and Heggarty (2001, p. 450)

How can you trade away accuracy to gain speed?

By using a simpler model!

process	model (physics)	model (ethics)
fast	impetus	Thomson-esque
slow	Newtonian	???

question 1

Why, if at all, are two systems better than one?

question 2

If being able to make
complementary speed-accuracy trade-offs
is one of the reasons why we have two systems,
which properties should we expect
to differentiate the two systems?

Thinking about speed-accuracy, can we justify these associations? I.e. If being able to make complementary speed-accuracy trade-offs is the reason why we have two systems, should we suspect that the systems have these properties?

implicit / modular
/ ‘system-1’ / ...

innate

informationally encapsulated

domain specific

subject to limited accessibility

speedy

tacit

subpersonal

unconscious

...

An immediate problem is, Which one or several of these features should we appeal to in characterising implicit mindreading? Everyone seems to have their own ideas.

To me, a more pressing problem is that ...

None of these properties can explain why there is an interaction with age with respect to particular measures of belief tracking,

Nor can they explain why there are dissociations in adults between performance on different measures.

For instance, what had domain specificity

or limited accessibility got to do with the fact that adults’ proactive gaze and response times fail to track false beliefs in some contexts? Would the theory be any different if proactive gaze were aligned with verbal responses?

conclusion

In conclusion, ...

There is evidence for fast and slow processes in physical cognition.

How do fast process influence slow judgements? Fast process can influence slow judgements via phenomenology.

Fast processes trade accuracy for speed; slow conversely.

Why are two systems better than one? Perhaps because they can make complementary speed-accuracy trade-offs.

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Speed-Accuracy Trade-Offs (in Physical Cognition)

Speed-Accuracy Trade-Offs (in Physical Cognition)

s.butterfill@warwick.ac.uk & c.sinigaglia

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