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.

Hint 7 of 8:

And there are counting machines near the shaft, on both levels of the lair.

Hint 8 of 8:

Press the button on the counting machine, and then select the number of dots
equal to the octospider number.  Once you get the number correct, the spikes
will extend, and you can go up or down the shaft.