# Design of a synchronized clock

I was living in a country where Internet wasn't that fast so the younger me had the following idea for compressing data

Let say 2 parties want to send data to each other, we know that data can be represented by a number literally any data no matter the size can be just a giant number.

So let say the 2 parties have this perfect synchronized clock and a very fast one, I mean a clock that can count billions of billions ( equivalent of gbits of data ) in a short amount of time.

So for party 1 to send data to party 2 it only need to send 2 messages : start counting and stop counting.

So any data can be sent using only 2 bits lol.

How hard is it to design that clock ?

• Well, billions of billions ticks per second is $10^{18}$ ticks/sec. This is approximately the max long number. It means, that your protocol allows one to send one long number per second. You can split it into chunks of $10^9$: and it means that you can send $10^9$ integers per second. And you can continue splitting it, limiting it to chunks of length $1$ or $2$ ticks: this way you'll be able to send $10^{18}$ binary signals per second. Therefore, you better of just send binary numbers.
– user114966
Jul 19, 2020 at 21:47
• Yeah I knew that, but by billions I really mean something that can count to gbits.
– user123664
Jul 19, 2020 at 21:51
• I've edited my comment. something that can count to gbits  I don't really understand what it means. Even if you have $10^{1000}$ ticks/sec, it doesn't help you (you'll be able to send something like $50$ longs per sec).
– user114966
Jul 19, 2020 at 21:52
• 1 gb of a known data is equal to a unique number a very big one so a counter for that.
– user123664
Jul 19, 2020 at 22:05
• Anyway, as you might've guessed looking at the numbers (which in your scenario is would be $2^{10^9}$ ticks/sec), the answer is "physically impossible". For a tick to occur, something must change inside the clock. And even if that changes happen within atom-level distances, particles must move far-far-far faster then a speed of light. There are other scenarios (like matter-energy conversion), but I can say without looking that they'll be equally impossible. Other things (such as radioactive decay) also don't happen anywhere near that frequently.
– user114966
Jul 19, 2020 at 22:15