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This quote keeps puzzling me.

I've newly started attending some lectures relating to the linguistic/information and theories of linguists past and present, which is usually followed up by a debate among the participants and the guest-lecturer of the day.

Though I usually enjoy these, the lecturer quoted Gregory Bateson half-way in, saying:

"The difference that makes a difference"

Which he quickly acknowledged as an extension of Donald MacKay's quote:

"Information is a distinction that makes a difference".

The problem was that the last quote confused the heck out of me.

What exactly did MacKay mean when he said "information is a distinction that makes a difference", anyway?

Could anyone explain what this quote meant?

An example would also be lovley, but is by no means mandatory.

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A linguistic example could be any classic minimal pair, like PIN/PEN. This is a distinction (/I/ vs. /E/), which makes a difference for the hearer: "Please hand me that pin." Because both 'pin' and 'pen' are valid options in that sentence, the way to get the correct message is to use that distinction.

This distinction could also fail to make a difference. If, for example, the word 'pin' did not exist (indeed, if English lacked the /I/-/E/ distinction entirely), then "Please hand me that pen." could be safely understood to refer to the object 'pin'. (This simplifies a little and assumes other minimal pairs aren't important.) In this case, the acoustic distinction is not missing, but it doesn't make a difference.

This concept is usually treated more formally in information theory, which might be a fruitful place to read more.

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This phrase is attributed to Donald Mackay but it doesn't seem to be possible to identify a source.

"A difference that makes a difference" on the other hand, is discussed at length by Gregory Bateson, as a definition of Information:

"The technical term "information" may be succinctly de-fined as any difference which makes a difference in some later event. This definition is fundamental for all analysis of cybernetic systems and organization. The definition links such analysis to the rest of science, where the causes of events are commonly not differences but forces, impacts, and the like. The link is classically exemplified by the heat engine, where available energy (i.e., negative entropy) is a function of a difference between two temperatures. In this classical instance, "information" and "negative entropy" overlap. Gregory Bateson Steps to an Ecology of Mind.Collected essays in anthropology, psychiatry, evolution, and epistemology more details

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A "distinction that makes a difference" seems like a tautologous expression to me, but I think what MacKay means is something along the lines of:

To transmit information, the sender and the receiver need to agree on what makes a difference and what doesn't.

E.g. if it hasn't been agreed that [ɪ] and [ɛ] are different (cf the pin-pen merger), then even if the sender makes a distinction, this will provide no extra information to the receiver.

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