# Time

## Problems

### practice

- To the nearest order of magnitude, determine the number of seconds that pass or have passed…
- in the life of an average human
- in all of recorded history
- since modern humans first appeared
- since the dinosaurs went extinct
- since the Earth was formed
- since the beginning of time

- Write something.
- Write something.
- Write something completely different.

### conceptual

- For each of the following questions, decide whether the question is asking for the time interval between two events or the time at which an event occurred.
- How long have you been waiting for me?
- How old are you?
- What time is it?
- When did that happen?
- When were you born?

### numerical

- London is usually five hours ahead of New York. Say it takes the Concorde two hours to fly from New York to London.
- What time is it when you arrive in London if you depart New York at 9:00 PM on the outgoing trip?
- How many hours have you lost? What will you do to make up for them?
- What time is it when you arrive in New York if you depart London at 9:00 PM on the return trip?
- How many hours have you gained? What will you do with them?

- The Network Time Protocol (NTP) is widely used to synchronize computers and other electronic devices connected to the internet. When your computer connects to a time server it is sent a 128 digit binary number. The first 64 bits are the number of whole seconds since the NTP era began. (The remaining 64 bits are the decimal portion.) David Mills, the creator of NTP, has reportedly said that the "64 bit second value is enough to provide unambiguous time representation until the universe goes dim."
Verify this claim by the following set of calculations.
- How many years is 2
^{64}seconds? - Find a value for the currently accepted age of the universe. (This has been relatively relatively easy since 2003 when several methods converged on a reliable number. Be sure to state your source.)
- How many more "ages of the universe" can we cycle through before NTP would need another binary digit?
- Find a claim for the expected lifetime of the universe. (This is slightly more difficult than part b. Work in this field is still speculative and values will be stated without much confidence. Be sure to state your source.)
- According to the value you found in part d, will NTP outlive the universe as we know it?
- If your answer to part e is "yes", give an approximate value for the time of the end of the universe in 64 bit binary seconds.
- If your answer to part e is "no", state the approximate fraction of the universe's expected life span that NTP will cover.

- How many years is 2
- Tom Duff at Bell Labs is reported to have said that "π seconds is a nanocentury". Show that he was more or less correct. (The nanocentury was invented at IBM as a software design objective — never let the user wait more than a few nanocenturies for a response.)
- The mathematician John von Neumann is reputed to have said that a lecture should never last longer than a "microcentury". How long is this in more familiar time units? Justify your answer.