Science > Division by Zero

Division by Zero

By LEONARD MCGAVIN
Published: May 4, 2008

The long battle against the division by zero may well be over now that the equation for the Theory of Everything (ToE) tears all of physics to shreds. As it turns out the division by zero problem is the greatest mathematical support for equation of the ToE.

Computers really don't like dividing by zero. Opening up the calculator application in XP and calculating, say 42 / 0, will equal the friendly message - "Cannot divide by zero". When trying to divide something by zero in a programming context, say using PHP, you'll strike an error something like - "Warning: Division by zero in divide_by_zero.php on line 1".

So what's the problem? The problem is that dividing something by zero is illogical in a computing terms. In general life, the concept also doesn't come up terribly often - "Could you give me a hand dividing this apple amongst zero people?"

By appearances the division by zero problem has at least 3 answers:

1) if you plot the division of a whole number by smaller and smaller numbers (Figure 1), say for instance, first dividing 1 by 1, then dividing 1 by 0.5, then dividing 1 by 0.25 you will notice an exponential scale start to form. As the dividing value gets closer to zero the resulting value gets exceedingly large. Now, as the dividing value goes past zero into negative territory the resulting value becomes a large negative number and becomes smaller as it approaches 1. It certainly seems possible to draw the conclusion that as the dividing number reaches zero the resulting number approaches an amazingly large number which could only be described as infinity.

2) in the real world using elementary arithmetic, it doesn't make a lot of sense if you attempt to divide a physical thing by fractions, by negative numbers or by zero. If you try to divide an apple amongst zero people nothing happens to the apple. The apple remains the same. Could it then be said that dividing an apple by zero leaves the apple whole, thus: 1 divided by 0 equals 1?

3) Or conversely, if you try to divide an apple amongst zero people, not one person receives any of the apple. Could it then be said that dividing an apple by zero leaves everyone with none of the apple, thus: 1 divided by 0 equals 0?

These are but three answers derived by different ways of looking at the division by zero problem. All answers are valid and show that it depends on a relative perspective that makes each answer meaningful in it's own way.

There are more ways than the three example given that can produce seemingly valid, not to mention, seemingly contradictory answers. Visit the fallacies based on division by zero on Wikipedia to find out more.

Science and Mathematics have always hated the idea of a paradox behind division by zero much like Einstein hated the consequences of the uncertainty principle. The paradox has been so disliked by Science and Mathematics that the problem has been scraped and given the blanket rule - "You cannot divide by zero".

The paradox itself is the basis for the ToE and it is only until the paradox is understood in terms of the ToE, that there ceases to be a paradox at all. As the paradox is understood it becomes apparent current computing, scientific and mathematical areas have given little thought to a major issue that has existed for a long time.

Comments

1. Zeus on May 19, 2008

McGovern, you should change your name to McGyver. You seem to be making it up as you go. Dividing an apple amongst zero people has never been done and we could all come up with possible answers. Perhaps it disappears, perhaps it turns into an infinite number of apples. When you do manage to do it, just be kind and let the rest of the world know. Or maybe, just keep it to yourself and leave us in our ignorance.

"You cannot divide by zero" because no-one has ever done it and no-one can agree on the theory of what may happen, by what you have mentioned previously as the basis of mathematics, peer review.

2. Field on May 20, 2008

My warmest of congratulations Luke! You have apparently discovered the theory of everything and it is almost exactly the same theory I've discovered!

I discovered that if 0 is the number that represents everything which does not exist then the reciprocal of 0 is the number that represents everything which does exist. in other words the equation for the toe is as follows

1/0=everything

It makes sense when you think about the fact that 1/0 means one thing divided by nothing. One thing divided by nothing means something that is undivided. And something that is undivided is the UNIFIED FIELD. Therefore the definition of 1/0 is the unified field theory. Therefore if the apple is divided by nothing it means the apple is just an inseperable part of everything else, the unified field.

Ha ha ha, this is great and I'm glad you discovered the same thing basically1 It makes me feel good.

The only thing I would say you got wrong is where you say that "as the dividing number reaches zero the resulting number approaches an amazingly large number which could only be described as infinity."

The way I would have said it would be "as the dividing number reaches zero the resulting number approaches a value which could be said to be equal to both positive and negative infinity"

If you are interested I will tell you why it is important to say it this way

ps. I also loved what you said about understanding the toe in terms of a paradox makes the paradox dissappear. I used to call this the "cosmic irony of truth and true paradoxes." One way I would illustrate this is by saying, for example, that contradiction is self-consistent. It's like saying time is constant change. It's a paradox in a way but once you understand it it makes perfect sense

cheers!

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