Why can't I ping from wireless to wired, but can from wired to wired?

I recently set up a home server (connected via ethernet) and I want to connect to it from my MacBook (which is on Wi-Fi). The problem is, my MacBook can not connect to my Linux based ThinkCentre. When I do a ping from any of those machines, arp -a shows (incomplete), and running sudo tcpdump -i any icmp on my linux shows no packets. So far, I get it, they can't find each other. The weird part happens when I try ping from both of these devices at the same time. After waiting for a bit, the MAC address gets resolved on both machines, and running sudo tcpdump -i any icmp on my lab shows the packe

Question by Khazho on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.