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June 6th, 2009, 02:46 PM  #1 
Newbie Joined: Jun 2009 Posts: 3 Thanks: 0  Hey gangto be honest...
Hi guys. I'm gonna be honest here. I'm awful at mathematics. Really terrible. And I joined, to ask you guys one question, which is as follows. If a person was to live nineteen years, and every day be given memories equal to every previous day, how many days would they have experienced? To further elaborate, this is for a story I'm writing. This person has been put into an artificial reality machine. They have, every day, woken up in a new identity. Each time, he has been given all the memories of the new identity as well as retaining his own. So, on his second day of real time, he had experienced three days of time, because he had experienced the real first day, the second real day and the false first day. So, as I am terrible at math and can't even begin to construct the formula for working this out, if this person was nineteen real time years old (we'll say to the day for simplicity's sake), how many days would he have experienced, including the false days added to his memories? Just to clarify, I do mean his 19th birthday, as in at the end of the first day he turns 19. 
June 6th, 2009, 04:48 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Hey gangto be honest...
1 + 2 + 3 + ... + n = n * (n +1) / 2. That's the essential part of math you need. On the first day of a person's nineteenth birthday, they've experienced 18 real years plus a day. That would include four or five leap years.* So 6575 or 6576 days. Using the formula above, that's 21,618,600 or 21,625,176 days, or almost 60,000 years. I'd be inclined to think a human would go quite insane after living maybe a thousand years, but that wouldn't work very well fictionally  they wouldn't even be 3 by the time that happened. * If the person was born before 1901 or after 2080, it's possible that they'd have experienced only three leap years. This doesn't change much, really. 
June 7th, 2009, 11:38 AM  #3 
Newbie Joined: Jun 2009 Posts: 3 Thanks: 0  Re: Hey gangto be honest...
Thank you very much! I simply could not wrap my head around this. Wow, the number is a lot higher than I had imaginedan almost 60,000 year old teenager...crikey. Don't worry about the insanity issue. He does insane 'on and off' many times, and an unlying madness is apparent in him even after he leaves his artificial reality. What makes it worse, is that every day he is put through a new form of torture. He wakes up at his physical age each day in a new identity, with only the false memories of that identity. He goes about normal life of that identity, and then something terrible ocurs to him, and in the process, all the other memories return. No matter how hard he tries to escape the horror, he always ends up 'dying' each day. He spends some time in a sort of limbo where he retains all his memories, only to wake up with a fresh body and mind. Not a very nice existence, but then, that's sort of the point. 
June 7th, 2009, 11:41 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Hey gangto be honest...
If you'd like to reduce the 60,000 years, you have a number of options: * Have this happen every week rather than every day; * Have this happen some days, but not all days; * Have it happen every day, but give him memory of only some days; * Make him younger than 19; * Fudge the numbers to improve the story. Of course you could also use it as inspiration instead and keep it at 60,000. Edit: Are you familiar with Descartes' demon? That seems relevant to your story as well. It might give you some ideas. 
June 7th, 2009, 11:56 AM  #5 
Newbie Joined: Jun 2009 Posts: 3 Thanks: 0  Re: Hey gangto be honest...
The 60,000 years is actually giving me a lot of ideasit gives me a lot more room to work with than my projections (which were waaaay offI was thinking something like three thousand at the most). One of the key ideas is that he goes so far beyond madness that he's recreated himself into insanity wrapped in a suit. Thinking about it, the longer time gives me a lot more wriggle room to let this idea developin this version, he could easily spend tens of thousands of years insane before forcing his way through it. And no, I hadn't read Descartes' demon argument, but the basic outline I can get from google fascinates me. Thanks for the tip! 
June 7th, 2009, 01:14 PM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Hey gangto be honest... Quote:
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