I'll just divide it all by zero.

There.

All gone.

You fool! Divide by zero makes it everywhere and everything!!! Ubiquitous! Eeegad, now you've done it.

Zinj

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- Thread starter lexmark
- Start date

I'll just divide it all by zero.

There.

All gone.

You fool! Divide by zero makes it everywhere and everything!!! Ubiquitous! Eeegad, now you've done it.

Zinj

Calling π "1" instead of "π" changes nothing. Relabeling is not simplicity.

Nope. As a transformation it simplifies the expression of rational multiples of pi. There are times when that can be useful.

In terms of the underlying relationships among values your statement has merit, however in terms of the possible expression of such relationships it does not. Relabeling can be tremendously simplifying. This is especially true, as in my prior example, when there is a transformation involved.

exempli gratia

Cartesian: (x,y)

Polar: (r,theta)

Cartesian: (0,0) = Polar: (0,x) { where 0 <= x <= 2*pi }

Cartesian: (0,1) = Polar: (1,pi/2)

Cartesian: x^2 + y^2 = 1

Polar: r = 1

Mark A. Baker

It is lovely to see someone who revels in their ignorance. The mystery is as much a pleasure as the knowledge that enables us to see it. That is the heart of a ScientistSoT - thank you for your explanation. I doubt that I will take 2 weeks off to study algebra either. In fact it would probably take me about 10 years to get a handle on it. My encounter with pure maths in first year university was enough to spin my mind permanently.

Further to your occasional sleeplessness, it always struck me as being really odd - well, bloody stupid really - that we could not accurately describe the circumference of a circle, given its radius. If you draw the circle from a radius, it has finite length and it can be measured with a ruler. Why can't it be calculated???

And.... capacitance, which is also an actual thing, has to be described using the square root of -1. What's this about???

If there is something wrong, it must be pretty basic.

If we were blessed with eleven figures instead of 10, or 7 or 16, would this make a difference? Have we been led down a mathematical dead-end because a chance mutation way back when gave us 10 fingers to count on, which led to a base 10 system?

In quantum physics, do you actually plug numbers into the equations, or is this 19th century thinking as well??

I'm sorry you are upset about pi. I too have a disappointment - with quantum mechanics. How dare the universe be so utterly inexplicable and apparently non-deterministic. It's a good thing I have very little grasp of it. It would be too much to bear otherwise.

I have heard it expressed that in studying a scientific discovery, you are able to recreate in your own experience the eureka moment where the original scientist made the discovery. You've just created the eureka moment that the Pythagoreans had. You have my sympathy.

Also, with regards your suggestion as to our possible digital deficiency, a number has the same properties no matter what numeral system we use. If 2+2=4 (And yes it is Will Smith), then 00000010 B + 00000010 B = 00000100 B. The only difference is that the numeral system that we have lends us to notice particular patterns. I remember a story about a soon to be prominant mathematician who was told to add up all the numbers between 1 and 100. So he added 99+1, 98+2, and realized that he could match up 1-49 with 51-99, giving him 49 groups which added up to 100 plus the leftovers - 50 and 100. This gave him 49 x 100 +50 + 100 = 5050. Needless to say, his teacher was disappointed that he didn't take longer to do it.

There are many properties of the number 9 in arithmetic that are apparent in the numerical system because of it's place as being the last digit. For example, if you get a number and reverse it and get the difference, it is always evenly divisible by 9. ie 4321 - 1234. But if we had 9 fingers, those same properties would be transferred to the number 8. So a different numeral system really only teaches us about itself.

That's why I am happy to have 10 fingers. I don't care how many they have on Markab.

This is the joy of tautologies!

May favourite tautology is Darwinism.This is the joy of tautologies!

As opposed to Evolution?

It's easy to see how it is almost a tautology. It says that the fitter organisms tend to survive, or rather, to reproduce in larger numbers. But when you ask, "Which are the fitter ones?", then in one sense the only answer is, "Those that reproduce more." So it may well seem tautological. But it is not, for one simple but subtle reason. The reason the only answer to "Which are fitter?" is, "Those who survive," is that it doesn't matter

What this means is that fitness does not actually mean

I think of evolution as being like football. You could say that football is a tautology, because the best team tends to win. And which team is the best? Why, the one that wins. And that's true. But sport is not really a tautology, because there is always some particular thing that makes a team win, not just an abstract 'winningness'. Any particular thing that produces wins will do. It doesn't have to be the passing game; it could be the running game. It doesn't have to be the quarterback; it could be the defensive line. In that sense, whatever makes the team best is just whatever makes it win. But it's not a tautology because winning isn't just winning as an abstract property, it's winning

Interesting post. Thanks.

It's easy to see how it is almost a tautology. It says that the fitter organisms tend to survive, or rather, to reproduce in larger numbers. But when you ask, "Which are the fitter ones?", then in one sense the only answer is, "Those that reproduce more." So it may well seem tautological. But it is not, for one simple but subtle reason. The reason the only answer to "Which are fitter?" is, "Those who survive," is that it doesn't matterhowthey manage to survive — whatever works, works. But here's the catch: however they manage to survive more, whatever gives them their edge, it has to besomething. Survival isn't just a matter of having a higher 'fitness' stat, like some crude role playing game system. If that were the case, then Darwinism would indeed be a tautology. But in fact there has to be some specific trait that puts the fitter organism over the top — longer neck, bigger brain, whatever, but something particular.

What this means is that fitness does not actually meanexactlyonly "tending to survive more". It means "having some particular trait that makes it survive more — though it doesn't matter what exactly the trait is, as long as it works".

I think of evolution as being like football. You could say that football is a tautology, because the best team tends to win. And which team is the best? Why, the one that wins. And that's true. But sport is not really a tautology, because there is always some particular thing that makes a team win, not just an abstract 'winningness'. Any particular thing that produces wins will do. It doesn't have to be the passing game; it could be the running game. It doesn't have to be the quarterback; it could be the defensive line. In that sense, whatever makes the team best is just whatever makes it win. But it's not a tautology because winning isn't just winning as an abstract property, it's winningsomehow.

Evolution has been shaped by the work of Gregor Mendel, Watson and Crick, and by Dawkins. By refering to it as Darwinism, I am referring to 'survival of the fittest,' which until I read the post under yours, I believed to be a tautology.As opposed to Evolution?

Thankyou.

It's easy to see how it is almost a tautology. It says that the fitter organisms tend to survive, or rather, to reproduce in larger numbers. But when you ask, "Which are the fitter ones?", then in one sense the only answer is, "Those that reproduce more." So it may well seem tautological. But it is not, for one simple but subtle reason. The reason the only answer to "Which are fitter?" is, "Those who survive," is that it doesn't matterhowthey manage to survive — whatever works, works. But here's the catch: however they manage to survive more, whatever gives them their edge, it has to besomething. Survival isn't just a matter of having a higher 'fitness' stat, like some crude role playing game system. If that were the case, then Darwinism would indeed be a tautology. But in fact there has to be some specific trait that puts the fitter organism over the top — longer neck, bigger brain, whatever, but something particular.

What this means is that fitness does not actually meanexactlyonly "tending to survive more". It means "having some particular trait that makes it survive more — though it doesn't matter what exactly the trait is, as long as it works".

I think of evolution as being like football. You could say that football is a tautology, because the best team tends to win. And which team is the best? Why, the one that wins. And that's true. But sport is not really a tautology, because there is always some particular thing that makes a team win, not just an abstract 'winningness'. Any particular thing that produces wins will do. It doesn't have to be the passing game; it could be the running game. It doesn't have to be the quarterback; it could be the defensive line. In that sense, whatever makes the team best is just whatever makes it win. But it's not a tautology because winning isn't just winning as an abstract property, it's winningsomehow.

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