The Garden Path To 1+1=3

When I disagree with another scientist, I sometimes respond, “In my professional opinion, this just looks 1+1=3 to me.” Maybe they took the garden path?

What is your answer to this simple math problem?


@Kevin and @Joel_Duff might like this article.


@zacharylawson, I’m pretty sure I said this in your podcast, didn’t I?

“The Garden Path To 1+1=3” is probably my new favorite essay on Peaceful Science.

Each paragraph of the article brought back memories of countless examples of 1+1=3 over the years, including my own blunders where my undeveloped intuition failed me.

When it comes to genomics, I’m unlikely to catch the errors in analysis. Same with complex taxonomy. But with linguistics, hermeneutics, and exegesis I generally do. If nothing else, my knowledge and experience has trained my intuition to at least raise read flags: “Something is clearly wrong in this person’s analysis of the Biblical text. I need to scrutinize it more closely.”

Joshua’s article brought a related peeve to mind: Some of the very same people who are stuck for years in 1+1=3 thinking (such as me with some topics, especially in my younger years) react to insightful expert critiques of their blunders with the all-too-easy retort: “That’s just mental gymnastics. I hope they don’t dislocate a shoulder or something!” A very famous radio preacher who thinks himself an expert theologian (despite a lack of training and experience) no doubt does think that the careful exegesis of an Koine Greek expert seems overly complex and convoluted. That much loved preacher is a dilettante and doesn’t know it. He doesn’t even understand some of the terminology. And he has no means to evaluate the important clues provided by Aramaic parallels and the value of consulting Moulton & Milligan when wrestling with a hapax legomenon. An expert’s analysis does sound like “mental gymnastics” to his untrained mind. He can’t follow the argument to see his glaring error.

No matter how much expertise we may accumulate in one field, there are plenty of others where we will still make 1+1=3 errors, in spite of our best efforts. It is a reminder of why the Dunning-Kruger Effect applies to everyone and not just "the ignorant masses."

There have been many times on Peaceful Science–especially when dealing with a sincere and yet somewhat tiresome PRATT—when I’ve asked myself, “Do I really want to try to summarize in a few paragraphs what took me thirty years of study to figure out?” For example, if someone has never wrestled with the inherent ambiguities of language and the complex problems of translation, how can I convert their 1+1=3 into 1+1=2 in a few sentences?

The only short answer to these issues is summarized in one word: humility. (And “Welcome to the human condition.”)


@sfmatheson the “garden path” was partly due a comment from you a while back. I hope you like the article.

Here is a great article that explains more about garden paths and how AI looks at them.

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Also, the ambiguities of grouping syllables into words can confuse the reader and/or listener—depending on the sentence. For example, consider this sentence:

“What is that in the road ahead?”

Does it mean:

“What is that in the road—a [decapitated] head?”


“What is that in the road [up] ahead?”

Big difference. Pauses when speaking can help—but how much of a pause (or lack of a pause) is needed to remove all ambiguity?

POSTSCRIPT: Speech therapists use computer software to play syllables of different “spacings” into the headphones of their young clients in order to help their brains learn to recognize word spacings.

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Speaking of another kind of linguistic garden path:

Some ancient Greek manuscripts (including classical Attic Greek and NT Koine Greek) don’t use spaces between words at all. After all, papyrus and other writing materials were very expensive so each page may be filled to the point of crowding. And lots of manuscripts lack any kind of punctuation. Some show only major stops (i.e. ends of sentences.)

Imagine being a scribe and having to copy an old manuscript that has no spaces dividing the words and no punctuation marks. The scribe must make judgments in separating the words and sentences (and perhaps delimiting important clauses with commas.)

Consider the difference a space can make—when two words are assumed to be three words instead, such as in 1 Timothy 3:16:

(1) Και ομολογουμενως μεγα. . . (KAI HOMOLOGOUMENOS MEGA. . .)
(2) Και ομολογουμέν ως μεγα. . . (KAI HOMOLOGOUMEN OS MEGA . . .)

The first one means “And confessedly great …” (As in the English idiom “Without question …”)

Second one means “We acknowledge how great …”

Long ago I could have listed several far more interesting passages where a word division makes a greater difference but this one was the first to come to mind.


3 posts were split to a new topic: What is Peaceful Science?

I think the Garden Path paradigm can be helpful in less abstract contexts.


Hehe, good one @BenKissling.

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Similar to the problem in the opening post, it is fascinating how the human brain can easily read a sentence where the first and last letter of each word is kept the same, but all of the letters between them are scrambled.

Human brains are heavily dependent on association and context, and it will even try to fill in blanks where there are no blanks. However, once you see the blank and know that it is empty you can’t help but see it. I could have sworn there were symbols in certain places in the opening post, but now I can’t help but see their absence. It’s a really great example of the inherent bias we all carry.


There are several different kinds of garden paths in this classic linguistic example: