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Without zero you couldn't measure anything with a ruler, there would be nowhere to start from. Extend that thought a little and you realize you couldn't count anything without zero. Spend a little more time and you see that there is nothing without zero.
Start with a singularity. Nothing? Well, zero is one number ... from nothing you've got two numbers already ... ... zero gives us the infinite, everything.
Start with a singularity. Nothing? Well, zero is one number ... from nothing you've got two numbers already ... ... zero gives us the infinite, everything.
Actually, a logical argument can be made that the non-digit "zero" is not necessary in classical mathematics. It's use is only as a place marker... i.e., a beginning place as described by Loosehead. The Babylonians seemed to have used a double mark from their stylus on clay tablets to indicate, say, a difference between 99 and 100. Rather than what I've just typed they would have indicated 1" ". They allowed the context to describe a starting place or a non-digit. It's only when the concept of algebra was introduced (probably in India) and advanced that the concept of, not only zero, but negative numbers became important.
Measuring things with, for example, a ruler doesn't require an actual "0". My roll up mesuring tapes do not have zero, for example, only a beginning mark. Space flight relies on planet, star and galaxy positions measured in a 'sanp-shot' that occurred in about 1975 rather than a zero-sum measurement of any kind... again a starting point only.
Another example is our date mesuring system. It's always been somewhat confusing since we measure from the first year after or beforethe birth of Jesus, not calling the actual year of His birth "zero".
Please understand, this is not an argument in favor of not recognizing the important concept, only that in actual everyday, non-algebraic use, it's importance is more of a fable
Measuring things with, for example, a ruler doesn't require an actual "0". My roll up mesuring tapes do not have zero, for example, only a beginning mark. Space flight relies on planet, star and galaxy positions measured in a 'sanp-shot' that occurred in about 1975 rather than a zero-sum measurement of any kind... again a starting point only.
Another example is our date mesuring system. It's always been somewhat confusing since we measure from the first year after or beforethe birth of Jesus, not calling the actual year of His birth "zero".
Please understand, this is not an argument in favor of not recognizing the important concept, only that in actual everyday, non-algebraic use, it's importance is more of a fable
Clanad, it is not at all confusing not to have an AD0; such an idea is absurd. How can you have a noughtth year of a man's life?
Although I know it is only nominal and not factual, AD1 is the year at the beginning of which Jesus was born (the first year of Our Lord). The previous year was 1BC (the first year, working backwards, Before Christ.)
Zero was the infinitesimal moment on the borderline between 1BC and AD1.
A failure to understand this is what led millions of people to spend colossal amounts of money celebrating the double Millennium a year early at midnight on December 31 1999 when it was actually on December 31 2000.
Although I know it is only nominal and not factual, AD1 is the year at the beginning of which Jesus was born (the first year of Our Lord). The previous year was 1BC (the first year, working backwards, Before Christ.)
Zero was the infinitesimal moment on the borderline between 1BC and AD1.
A failure to understand this is what led millions of people to spend colossal amounts of money celebrating the double Millennium a year early at midnight on December 31 1999 when it was actually on December 31 2000.
Not surprisingly, chakka35, we have a disagreement... not uncommon is such discussions, no? Fact is there is no AD1 or BC 1 until the completion of that year. For all of either year, we may wish to call it 1BC or AD1 but it is neither. It could only be a fraction of the 12 month period. And, as far as attribution of a "nought" (love the British expressions) to a man's birthday, you yourself explain that just such a "nought" is the "infintesimal moment on the borderline between 1BC and AD 1"... I, of course, maintain that there is no such "infinitesimal moment' because AD1 or BC1 are separated by 24 months. Each year on either side is Year Zero ,until 12 months has elapsed. Wikipedia agrees, saying "...This means that between, for example, 500 BC, January 1 and AD 500, January 1 there are 999 years: 500 for the time taking place BC, and 499 for the part of AD. common usage Anno Domini 1 is preceded by the year 1 BC, without an intervening year zero..." However, if a person on this side of the dviding line talks about something happening 6 months BC they cannot be referencing 1BC simply because that hasn't occured yet.
Now, if we used Ordinal numbers instead of Cardinal numbers, some (but not all) of the problem would be aleviated...
Now, if we used Ordinal numbers instead of Cardinal numbers, some (but not all) of the problem would be aleviated...
I can't help feeling Clanad, that you are confusing the concept of zero with the symbol for zero. If, as you say, the Babylonians left a space instead of making a mark, then in that position the space symbolised zero.
squarebear, perhaps you would like to try doing some simple maths using Roman numerals :-)
squarebear, perhaps you would like to try doing some simple maths using Roman numerals :-)
The example of the abacus is a false one. The place value uses of zero are taken care of by the fact that the wires of the abacus are spaced left to right. The "rest" position of the abacus, with all the beads at the bottom of the wires is logically equivalent to zero. An abacus bead only gains a value when it is flicked up. The Chinese abacus has five unit beads in the lower register and two five beads in the upper. The Japanese realised that this was overkill and only have four beads in the lower and one in the upper. This makes the actual moving of the beads faster and approaches or exceeds the operational speed of an adding machine - only without the benfit of a till roll!
I am genuinely astonished, Clanad, that someone as intelligent as you in many other respects can get this matter so spectacularly wrong.
The first year of your life is that 12-month period between the moment of your birth and your first birthday. The first minute, the first hour, the first day, week and month are all steadily-increasing fractions of that first year. At the end of the 12th month, the first year is complete. To suggest that the first year does not start until then is ridiculous.
So if our calendar were based on your life, that first year would be AC1 - Annus Clanadus 1. The previous year would be The First Year before Clanad - 1BC. So we would go straight from the end of 1BC to the beginning of AC1. What could AC0 possibly mean?
You seem to imagine that a year has no existence until it is complete, that it cannot have fractions. But that is like saying that until your car's odometer registers a complete mile, you haven't moved!
The first year of your life is that 12-month period between the moment of your birth and your first birthday. The first minute, the first hour, the first day, week and month are all steadily-increasing fractions of that first year. At the end of the 12th month, the first year is complete. To suggest that the first year does not start until then is ridiculous.
So if our calendar were based on your life, that first year would be AC1 - Annus Clanadus 1. The previous year would be The First Year before Clanad - 1BC. So we would go straight from the end of 1BC to the beginning of AC1. What could AC0 possibly mean?
You seem to imagine that a year has no existence until it is complete, that it cannot have fractions. But that is like saying that until your car's odometer registers a complete mile, you haven't moved!
The experts don't always agree on the date of Jesus' birth, but the concensus seems to be sometime in Spring, between March and May. The year seems in doubt too, up to six years earlier depending upon the authority.
Early Christians celebrated Christ's death and resurrection rather than his birth. December 25th was chosen a long time later ... possibly with the added bonus of lightening the harsh Winter (and the times) with a (fairly) universal feast.
Today it's not much different, except the reason. Our current leaders and thinkers expect us to praise the High Street.
But back to zero. Without it there is nothing. Every fundamental concept we have uses it - you don't get owt for nowt. The conservation laws, thermodynamic laws ... every description of the universe includes zero. Whether or not you use a symbol couldn't be more irrelevant, it is still there.
That the Romans didn't use zero is a great myth. They may have lacked a symbol, but when you put one brick on top of another you make something that includes zero in its definition.
It's not a question of choice, it is there.
Early Christians celebrated Christ's death and resurrection rather than his birth. December 25th was chosen a long time later ... possibly with the added bonus of lightening the harsh Winter (and the times) with a (fairly) universal feast.
Today it's not much different, except the reason. Our current leaders and thinkers expect us to praise the High Street.
But back to zero. Without it there is nothing. Every fundamental concept we have uses it - you don't get owt for nowt. The conservation laws, thermodynamic laws ... every description of the universe includes zero. Whether or not you use a symbol couldn't be more irrelevant, it is still there.
That the Romans didn't use zero is a great myth. They may have lacked a symbol, but when you put one brick on top of another you make something that includes zero in its definition.
It's not a question of choice, it is there.
I don't, for a moment, doubt the genuiness of your astonishment, chakka35, but now my confusion must match you astonishment, since what I've iterated is precisely the example you presented in your first post. You said "... a failure to understand this is what led millions of poeple to spend collosal amounts of money celebrating the double Millenium a year early at midnight December 31, 1999 when it was actually on December 31, 2000..."
Which precisely supports my contention that a new century doesn't begin counting year 1 until one year has been accomplished. When we count, we count at 1. This seems such a simple premise, but its caused quite a bit of confusion when trying to figure out the demarcation for the centuries and the millennia occur. 1901 began the 20th Century, 2001 began the 21st century. The last year of the 21st century will be 2100.
Actually, for the sake of accuracy, we should note that uur current numbering of years was instituted around 526 AD, by the Roman and Christian Monk Dionysius Exiguus... so we have him to blame.
Look, I'll magnaminously meet you half way (no pun intended)... I'll agree to eliminating the term year zero if you agree that no year 1 (either BC or AD) could be called such until 12 months had passed from the point of demarcation. There can be (as I've already stated) a <i.fraction of year one (1) but there can be no such year 1 until it's been completed, you can't be one year old until you've reached....well... one year old...deal?
Which precisely supports my contention that a new century doesn't begin counting year 1 until one year has been accomplished. When we count, we count at 1. This seems such a simple premise, but its caused quite a bit of confusion when trying to figure out the demarcation for the centuries and the millennia occur. 1901 began the 20th Century, 2001 began the 21st century. The last year of the 21st century will be 2100.
Actually, for the sake of accuracy, we should note that uur current numbering of years was instituted around 526 AD, by the Roman and Christian Monk Dionysius Exiguus... so we have him to blame.
Look, I'll magnaminously meet you half way (no pun intended)... I'll agree to eliminating the term year zero if you agree that no year 1 (either BC or AD) could be called such until 12 months had passed from the point of demarcation. There can be (as I've already stated) a <i.fraction of year one (1) but there can be no such year 1 until it's been completed, you can't be one year old until you've reached....well... one year old...deal?
Phew, Clanad, I�m glad we agree that the 21st Century and Third Millennium started on January 1st 2001. I don�t what made me think that we disagreed on that.
(The situation in UK was very odd at that time. All the knowledgeable authorities agreed on the correct date � I know because I wrote to them all! These included Whitaker�s Almanack, the Greenwich Observatory (in Cambridge and in Hawaii), the professor running the Millennium Clock at Greenwich, and my local Trading Standards Officer who agreed with me that an advertisement in an up-market national newspaper offering holidays on the other side of the world �to see in the millennium first� were fraudulent because the dates were December 1999/January 2000. He threatened the paper with the law and they withdrew the ads and cancelled a competition connected to it.
Also in agreement was the government. So when I asked the government why, if they knew the correct date, their official celebrations were a year early, they said that �that�s what the public want! So a government that was elected on a cry of �Education! Education! Education!� was happy to tell children that a century comprised 99 years and not 100. Dear, dear.)
Although I agree that a first year is not complete until 12 months have elapsed, the earlier months are all part of that first year and no other: the first four weeks of your life formed the first month of your first year.
If I boast that I am going to run 100 miles non-stop at 5 mph and drop dead after 880 yards the front-page headlines that would flash around the world would say CHAKKA35 COLLAPSES HALF-WAY THROUGH HIS FIRST MILE!
Getting back to zero, I hope you agree that the rule is:
We start counting at zero but not with zero. Zero is the nothingness we start with; the counting starts with 1.
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