When you want to move one position to the left, execute the following algorithm:

• Mark the current position as special.
• Move to the origin.
• Translate the tape one cell to the right, while keeping the special marker in place.
• Move to the origin.
• Scan until reaching the special marker.
• If you move to the right, don't forget to erase the special marker.

When you want to move one position to the left, execute the following algorithm:

• Mark the current position as special.
• Move to the origin.
• Translate the tape one cell to the right, while keeping the special marker in place.
• Move to the origin.
• Scan until reaching the special marker.
• If you move to the right, don't forget to erase the special marker.

(This simulates a Turing machine with a single two-sided tape.)