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YouTube video (just click the link and it will automatically fast-forward to the right time mark for you which is located at about 9 minutes 50 seconds)

Transcript:

More of an astonishing nature. Here is a cork stopper. Here is a cork stopper with a pin in it and there's the head of the pin. Here's another cork stopper with a pin in it and that's the point of the pin. And if I put these point to head in this position, if I can find that position here, and let go, obviously it will not stay stably. It will tip over.

I'm not sure what he exactly means by that.

Still picture from the video:

picture from the video

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    Look at it as "And if I put these point-to-head in this position, if I can find that position here, and let go, obviously it will not stay stably. It will tip over." How do I position these constructions? "I'm positioning them point-to-head. I'm putting them in a point-to-head position." It's a bit like the expression side-by-side: "let's put them side-by-side." – CowperKettle Sep 23 '15 at 11:56
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The cork in the bottle has a pin in it with the point in the cork and the head of the pin sticking out.

It's never very visible in the video, but as your excerpt explains, the pin in the second cork is turned the other way: the head is in the cork and the pin's point is sticking out.

So the lecturer places the point of the second pin on the head of the first pin: he places them point to head.

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He means putting them together with the point of one against the head of the other.

It's not an idiom, he means it literally.

However, it does use a grammatical device that might not be obvious: we can make modifying phrases which behave like adverbs from nouns (usually parts of something) without articles, and a preposition or conjunction, as:

head to head

side by side

head to toe (meaning "from the head to the toe", i.e. the whole body)

ear to ear (used of a smile, meaning very wide)

As you can see from these examples, sometimes the meaning is literal and obvious, but sometimes it is idiomatic.

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