[Humanist] 31.149 pubs: on maths for humanists; digital logic

Humanist Discussion Group willard.mccarty at mccarty.org.uk
Fri Jun 30 08:42:00 CEST 2017


                 Humanist Discussion Group, Vol. 31, No. 149.
            Department of Digital Humanities, King's College London
                       www.digitalhumanities.org/humanist
                Submit to: humanist at lists.digitalhumanities.org

  [1]   From:    Gabriel Egan <mail at gabrielegan.com>                       (66)
        Subject: Re: [Humanist] 31.145 pubs: mathematics for the humanist

  [2]   From:    Willard McCarty <willard.mccarty at mccarty.org.uk>          (30)
        Subject: Logic of the Digital


--[1]------------------------------------------------------------------------
        Date: Thu, 29 Jun 2017 08:30:42 +0100
        From: Gabriel Egan <mail at gabrielegan.com>
        Subject: Re: [Humanist] 31.145 pubs: mathematics for the humanist
        In-Reply-To: <20170629050600.EC752675E at digitalhumanities.org>

In Patrick Juola and Stephen Ramsay's new book _Six Septembers_,
announced here, there is a most interesting discussion of
the notion of the Null Hypothesis (pp. 246-9). They take as
their example a hypothetical cat that weighs 40 pounds,
which is much more than would be normal for a Siamese cat. They
provide a table of data showing the weights of 100 Siamese cats,
in which 85 cats weighed 5 pounds or more, 50 cats weighed 10
pounds or more, 30 cats weighed 15 pounds or more, 15 cats
weighed 20 pounds or more, 7 cats weighed 25 pounds or more,
2 cats weighed 30 pounds or more, and no cats weighed 40 pounds
or more.

The Null Hypothesis is that this 40-pound cat is a Siamese. Juola
and Ramsay write about the data just mentioned:

<< This table, then, gives us an estimate of the probability
that if the cat sitting in front of you were Siamese, it would
weigh as much as it does (or more). >> (pp. 248-9).

This seems to me to be problematic as a statement. The probability
that (if some hypothesis is true) the cat would weigh as much as it
does is surely 100%, since we can be quite sure that the cat does
indeed weigh as much as it does. That necessity is built into
the English phrase "weigh as much as it does". The matter of
likelihood surely applies not to the cat's weight (which
is certain) but rather to its breed (which is uncertain).

I realize that this might seem like a quibble about terminology, but
I don't think it is. I think there is some more pervasive inversion
of logic going on here. Juola and Ramsay rightly say that the
probability value implied by the data give us "the probability
that the observed data would be seen if the null hypothesis
were true". But then they follow this with the assertion that:

<< At this point, the test becomes simple logic. If the cat were
an ordinary Siamese, it would probably not weigh forty pounds.
Therefore, if it does weigh forty pounds, it's probably not an
ordinary Siamese. >>

This statement seems to me to commit a well-known fallacy. The
probability value is a remark on how often the observed data
should be expected if the Null Hypothesis is true, not a remark
on the truthfulness of the Null Hypothesis.

To see why we cannot safely move from their premise (the infrequency
of the observed data being observed) to their conclusion (that the
Null Hypothesis is untrue), take the case of a lottery. Our
Null Hypothesis is that the lottery is run purely on chance
with no cheating or bias, or in other words that it is 'fair'.
Suppose that the likelihood of my one ticket winning this
lottery, if it is 'fair', is less than one chance in a million
(p < 0.000001). And suppose I do indeed win with my one
ticket. If I were to follow Juola and Ramsay's logic I would
argue like this:

<< At this point, the test becomes simple logic. If the lottery
were fair, my ticket would be very unlikely to win. Therefore,
if I do win, it's very unlikely to be a 'fair' lottery. >>

This is clearly a false conclusion, but I got to it using
precisely the logic that Juola and Ramsay tell us to use.

Did I go wrong somewhere, or are Juola and Ramsay indeed
committing a logical fallacy here? I have a personal interest
in this that explains why I turned straight to their account
of the Null Hypothesis, since such logic has recently been
used to much rhetorical effect in my own specialized area,
which is authorship attribution by internal evidence. It
matters to me whether I'm understanding this topic
properly or not, and I'm genuinely asking members of this
list to correct me if I'm mistaken.

In raising this question, I make no critique of any other
part of Juola and Ramsay's book and I should record that I
applaud their making it available via Green Open Access.

Regards

Gabriel Egan



--[2]------------------------------------------------------------------------
        Date: Thu, 29 Jun 2017 10:57:53 +0100
        From: Willard McCarty <willard.mccarty at mccarty.org.uk>
        Subject: Logic of the Digital
        In-Reply-To: <20170629050600.EC752675E at digitalhumanities.org>

Allow me to draw to your attention a relatively new book of which I just 
became aware: Aden Evens, Logic of the Digital (Bloomsbury, 2015). I 
quote its first paragraph and a snippet from a bit further on:

> All digital technologies share one thing: they operate on the basis
> of a discrete code. Usually this code is binary, constructed from
> sequences of binary digits or bits, each of which can be in one of
> two states, named 0 and 1. The most basic contention of this book is
> that the binary code, which defines and enables digital technology,
> is consequential; the 0s and 1s that allow a machine to operate 
> digitally lend to that machine something of their character or way of
> being. Logic of the Digital articulates this ontology, describing how
> the binary code reveals itself throughout the digital and so also in
> the thought and action of those who live with and within digital
> technologies.
 > ...
> A code such as the binary code is not a neutral surface of
> inscription but lends its character to the objects and actions it
> encodes.... This is not a technological determinism... The digital
> makes an excellent companion to rationalist epistemology,
> instrumental reason, positivist notions of truth...

Those who argue that digitality does not matter have something to argue 
against.

Read it tonight!

Yours,
WM

-- 
Willard McCarty (www.mccarty.org.uk/), Professor, Department of Digital
Humanities, King's College London; Adjunct Professor, Western Sydney
University and North Carolina State University; Editor,
Interdisciplinary Science Reviews (www.tandfonline.com/loi/yisr20)




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