The Third Millennium

Date: 01/23/2000 at 21:09:09
From: Bruce Hutchison The Big Picture
Subject: When does the 3d Millennium begin?

Hello Dr. Math,

My name is Bruce Hutchison. I am the anthropologist co-host of a new, 
nationally syndicated public radio program called "The Big Picture" 
with Bruce and Melissa. Anthropologist Melissa Farncomb and I look at 
why people do the things they do, across time and cultures (usually in 
a lighthearted way)! We're recording this week's show on The 
Millennium and Prophesies. We have two questions for you for our show, 
to which we'd be delighted to give you credit:

1. When is the "true" millennium, and why?

2. Although we think of numerical systems as completely rational 
   (pardon the pun), are there any inherent predictions or 
   unverifiable assumptions within math?

In addition to your email response, or possibly in place of it, we 
would very much like to do a fairly short recorded interview with you 
(five minutes or so) on these questions.

Bruce Hutchison
The Big Picture

Date: 01/25/2000 at 01:38:21
From: Doctor Ken
Subject: Re: When does the 3d Millennium begin?

Hi Bruce,

Glad to help out, I'm a public radio fan myself. My name is Ken 
Williams, and though I can't speak for all the Dr. Math volunteers 
(there are over 200 people who can answer Dr. Math questions these 
days), I'm the founder of the service, so sometimes I take on these 
kinds of spokesperson duties.

Regarding the first question about when the "true" millennium begins, 
I actually believe that's a better question for an anthropologist than 
a mathematician. The word "millennium" simply means any period of 1000 
years, though it's natural for us humans to want to start some 
millennium at a known point in history and keep dividing the eons into 
consecutive millennia thereafter.

Therefore, if we're going to talk about a "true" millennium, we should 
probably fix some important event in the past and count forward 1000 
and 2000 years. Supposedly, we've done this with the birth of Christ. 
Seems simple enough - just count forward 2000 years from the nativity, 
and pencil in a millennium celebration on the calendar.

Well, the problems with that are numerous. First, since our years are 
actually enumerated as "the 1999th year of our lord," it seems we 
actually started counting at the year 1, i.e. "the first year of our 
lord."  That's essentially the argument of people who say the 
millennium begins next year.

Did we actually start counting like this, from the year 1? Of course 
not - the present-day Gregorian calendar, which is reasonably accurate 
and reliable, wasn't adopted until the year 1582 AD (for 
English-speaking countries). Before that, people used the Julian 
calendar, which had been in use since about 4 A.D. and was 
recalibrated in about 527 A.D. to count years from the birth of 
Christ. Previously it counted from the founding of the Roman Empire. 
To perform this recalibration Roman scholars did the best they could, 
but modern scholars seem to think they were off by a few years.

Furthermore, 10 or 11 days were actually deleted from the calendar in 
1582 when we shifted to the Gregorian calendar - should we adjust for 
those too, and have the big party on Jan. 10, 2002? I think not.

And finally, if Christ was actually born on Dec. 25, then _that_ year 
can be considered "the first year of our lord," i.e. the first year of 
the new millennium, and the following year (year 1) is the second. 
Which would imply that 2000 ushered in a new millennium.

In short, since the historical/calendric situation is so messy, I 
believe that we should measure the millennium by noticing when the big 
party is, and Prince doesn't party like it's 2000. I think we're in 
the new millennium now.

It's also worth noting that since there was no year zero, the years 
transitioning from BCE to CE are numbered ... -3, -2, -1, 1, 2, 3, ... 
But some people, notably astronomers, want the math to work out 
better, so they actually use a year zero (... -2, -1, 0, 1, 2, ...), 
so they're one year off from the rest of us in negative-land.

You can find a lot of information about this stuff at 

  The Calendar - Royal Observatory, Greenwich
  http://www.rog.nmm.ac.uk/leaflets/calendar/calendar.html   

and

  The Julian and the Gregorian Calendars - Peter Meyer
  http://www.magnet.ch/serendipity/hermetic/cal_stud/cal_art.htm   


Now, about your second question. Yes, there are certainly things in 
mathematics that are unproven, and these generally fall into three 
categories:

(1) Simple statements that we accept without proof;

(2) Statements that we simply haven't been smart enough to prove or 
    disprove yet;

(3) Statements that cannot be proven true or false.

Statements of type (1) are called "axioms," and they're the 
fundamental building blocks of mathematics. They're obvious statements 
like "1 is not equal to 0," or "given two points, exactly one line 
goes through them." If we accept these basic statements as our 
foundation, we can prove all other provable results from them. So in a 
sense, unproven statements are right at the heart of mathematical 
thought. In fact, mathematics _never_ says anything is true - it only 
says that certain things are true IF you accept the basic axioms. This 
isn't really a problem, since the axioms are usually so obvious that 
most people accept them without qualms.

There are some cases in which assuming different sets of axioms will 
give you different bodies of mathematics, and that can be fun. For 
example, this is the difference between Euclidean and Hyperbolic 
geometry; one simple axiom about parallel lines is changed, and it has 
huge effects on what the resulting body of mathematics looks like.

Statements of type (2) are pretty tough, but we'll crack 'em. :-)

Statements of type (3) are things that can make you question your 
place in the universe. An Austrian mathematician named Kurt Godel 
proved in 1931 that there must be statements of mathematics that 
cannot be proved or disproved. The somewhat irritating thing is that 
we don't know which statements these are. The main thing that 
mathematicians get out of this is that the forest of mathematics is a 
complicated one indeed, and we'll never completely know its landscape.

I look forward to talking with you.

- Doctor Ken, The Math Forum
  http://mathforum.org/dr.math/   

Date: 01/25/2000 at 02:20:56
From: Bruce Hutchison
Subject: Re: When does the 3d Millennium begin?

Ken,

Excellent responses. We're looking forward to talking to you tomorrow. 
Thanks again.

Bruce