How do I climb the shaft with the retracted spikes?

Hint 1 of 8:

You can't climb it while the spikes are retracted.

Hint 2 of 8:

But something in the octospider lair will extend the spikes.

Hint 3 of 8:

The spikes seem to be controlled by a mechanical device.  Have you seen or
heard any other mechanical devices?

Hint 4 of 8:

Something makes a loud clicking noise whenever you step on the circles just
in front of the ramp out of the lair and in the room next to the subway on
the lower level of the lair.

Hint 5 of 8:

Try looking at the ceiling above those circles.

Hint 6 of 8:

There is a picture of some extended spikes just next to an octospider number;
the number is on the right side of the circle.