Spiny Norman

02-02-2005, 09:30 PM

WARNING: Some may interpret this as a "troll". Well, it sort of is, but then again, its not really, I'm just having a bit of fun because I like logic and mathematics.

As I drove to work this morning in some of the worst summer weather that I have ever seen in Melbourne (lowest February maximum temperature since they started keeping records, pelting rain, more rain, and yet more rain), I pondered some of the recent complicated discussions about genetics and evolution, the nature of the universe, whether God exists, etc. Fascinating stuff. Yet my mind turns inexorably to the subject of mathematics ... and this is something that I know is of particular interest to a number of other board denizens.

Now maths has always been the love of my life (present spouse not withstanding!). Back when I did high school it was still split out into Pure and Applied. Lord only knows what they've done to it nowadays! Applied maths was always my strength. I loved the problem solving bits such as:

Bill (not our Bill) weighs 75 kilos. He climbs a ladder set at an angle of NNN degrees to the perpendicular which is leaning against a wall. The coefficient of friction is blah blah blah, etc ... how high can Bill climb the ladder before it slips?

But all of that is all too difficult for a bear of very little brain such as myself, so I have resolved in my own mind to post the following questions and invite your responses. I have decided to restrict myself to only ask questions about ONES and ZEROS. Anything else would be far too complicated and, therefore, not much fun!

Q1. Where did the concept of ZERO come from?

You see, I can see ONE apple. But I can't see ZERO apples. Quite irrational really. So it strikes me as particularly abstract. My recollection is that, once upon a time, there was no concept of zero but someone "invented it". Perhaps it was one of those fundamentalist Greeks? No matter whether I start with ONE apple and then take that apple away, or whether I start without any apples and add ONE apple, it still doesn't make sense when someone says I have ZERO apples .... I keep telling them, plain as the quite substantial nose on my face, that I can't have ZERO apples because I clearly haven't got any apples at all, so I just challenge them to show me the ZERO apples. At that point they start throwing things at me and calling me names.

Q2. Can it be proven that ZERO exists?

I can't see it, so how can I be sure that its not a conspiracy of scientists or mathematicians leading me astray.

Q3. What about dividing ONE by ZERO?

I know that when you divide ONE by ever smaller numbers, the resulting answer gets larger and larger ... but when I divide ONE by ZERO they tell me that I don't get a number, I get an answer that isn't really a number after all ... I really get a "concept" called infinity.

Q4. Where did this concept of ONE divided by ZERO come from?

I'm pretty confident in suggesting that nobody has ever seen anything that is infinite, because everything that I've ever seen has existed within the constraints of three dimensions (four if you count time).

Don't get me started on the square root of MINUS ONE or my head will explode, because all of a sudden you start getting answers that are a bit wishy-washy (e.g. the answer is PLUS or MINUS ONE ... I mean, hello, would someone please make up their mind, that's just not rational)!

All very confusing. I'm sure someone will be able to help me out.....

As I drove to work this morning in some of the worst summer weather that I have ever seen in Melbourne (lowest February maximum temperature since they started keeping records, pelting rain, more rain, and yet more rain), I pondered some of the recent complicated discussions about genetics and evolution, the nature of the universe, whether God exists, etc. Fascinating stuff. Yet my mind turns inexorably to the subject of mathematics ... and this is something that I know is of particular interest to a number of other board denizens.

Now maths has always been the love of my life (present spouse not withstanding!). Back when I did high school it was still split out into Pure and Applied. Lord only knows what they've done to it nowadays! Applied maths was always my strength. I loved the problem solving bits such as:

Bill (not our Bill) weighs 75 kilos. He climbs a ladder set at an angle of NNN degrees to the perpendicular which is leaning against a wall. The coefficient of friction is blah blah blah, etc ... how high can Bill climb the ladder before it slips?

But all of that is all too difficult for a bear of very little brain such as myself, so I have resolved in my own mind to post the following questions and invite your responses. I have decided to restrict myself to only ask questions about ONES and ZEROS. Anything else would be far too complicated and, therefore, not much fun!

Q1. Where did the concept of ZERO come from?

You see, I can see ONE apple. But I can't see ZERO apples. Quite irrational really. So it strikes me as particularly abstract. My recollection is that, once upon a time, there was no concept of zero but someone "invented it". Perhaps it was one of those fundamentalist Greeks? No matter whether I start with ONE apple and then take that apple away, or whether I start without any apples and add ONE apple, it still doesn't make sense when someone says I have ZERO apples .... I keep telling them, plain as the quite substantial nose on my face, that I can't have ZERO apples because I clearly haven't got any apples at all, so I just challenge them to show me the ZERO apples. At that point they start throwing things at me and calling me names.

Q2. Can it be proven that ZERO exists?

I can't see it, so how can I be sure that its not a conspiracy of scientists or mathematicians leading me astray.

Q3. What about dividing ONE by ZERO?

I know that when you divide ONE by ever smaller numbers, the resulting answer gets larger and larger ... but when I divide ONE by ZERO they tell me that I don't get a number, I get an answer that isn't really a number after all ... I really get a "concept" called infinity.

Q4. Where did this concept of ONE divided by ZERO come from?

I'm pretty confident in suggesting that nobody has ever seen anything that is infinite, because everything that I've ever seen has existed within the constraints of three dimensions (four if you count time).

Don't get me started on the square root of MINUS ONE or my head will explode, because all of a sudden you start getting answers that are a bit wishy-washy (e.g. the answer is PLUS or MINUS ONE ... I mean, hello, would someone please make up their mind, that's just not rational)!

All very confusing. I'm sure someone will be able to help me out.....