Dennisg

I had a quick look at Taylors theorem - I think I could cope if there was a bit of verbage explaining things. It look more of a way of estimating a value rather than a way to directly calculate one.

Thanks, any will do - how about one that you are most comfortable with?

EEK!!!! get away from me! Can you explain the logic behind such equations. Thanks.

I agree that Darwin is a kind of symbol or focal point for evolution and evolution is the work of many scientists. My understanding is that he could not reconcile the cruelty he saw in nature with the concept of a good and loving God. He removed the idea of God from the natural world but maintained that God was still valid for human ethics.

I found this interesting debate: http://www.arn.org/docs/orpages/or161/161main.htm Provine is very anti God - I wonder why this is such a hot issue. Is this the chart? http://www.bio.miami.edu/dana/pix/comparative_embryo.jpg

Thanks for your post. I'm still processing it - this part is the most interesting. It may help - how exactly is pi calculated? Interesting that a ratio is used to calculate area etc. I'm interested in how the ratio is calculated.

Thanks

I am trying really to understand your logic but you are talking in circles (no pun intended). Your replies sound like an exercise in medieval scholasticism mixed with 20th century psychological “living in denial”. Really. By defining pi = pi you have simply closed your minds to any original and fun thinking on the topic. It sounds absurd for you to say that an infinite series of non repeating integers is knowable. Completely equivalent? Just need to fill in a few intergers and she's sweet:eyebrow: Sloppy thinking at best and self deception at worst.

. Thanks I am no expert on Darwin’s ideas. My understanding is that he thought that one member of a species would have a chance mutation and that this mutation would give this member a better chance at survival and reproduction. The offspring of this member would then become isolated and the advantageous trait would become dominate in the species. This process of change would continue until breeding became impossible with members of the “old” species and that would signal the emergence of a new species. Gradualism, geometric v. exponential growth, inheritance of acquired characters are the building blocks that Darwin used to build his theory. But what interests me the most is why he came up with the scenario that he did. Other scenarios are possible using these same observations. Did the Victorian industrial culture influence the way he saw nature?

Unless you mean n = n then you have lost me. And if that is what you mean then God help you. Thanks for letting me read this after you were done. I have read it before. If pi is an infinite series of non repeating integers then I don’t think that you can say its value is exactly known – please correct me if I am wrong. There are a couple of points here that I think are interesting and worth discussing. 1. The area of an object in a plane is determined by lines and not points. This being the case then the notion of a “round” circle is fantasy unless the lines are dimensionless objects. 2. The practical out come of pi being irrational is that there are many different values for pi in use. It could be that pi is not a constant but its value varies with the radius of a “circle”.

Yes, but pi is not known exactly thus neither is the area. The boundary of a circle is made up by a set of points of which no line can be formed that includes more than two points. The boundary of a square is made up by points that can be defined by just 4 lines. When the definition of a point is dimensionless then the number of lines that can be derived from a circle in infinite and thus pi become irrational. But if the definition of a point has a finite dimension I am guessing that pi will become rational

I agree that shapes such as squares and circles do not naturally occur. What interests me is why pi is an irrational number. This means that the exact area of a circle can never be known. Why is this? We can know the exact area of a square etc but not a circle. Maybe an irrational number is nature’s way of telling us that we have got something basic wrong - in this case the definition of what a "point" is. I think for a point to occupy a location it must have a dimension.

Thanks guys

I was wondering if anyone has done some research into this topic. I know there are some quick answers to this question but I think the topic deserves a lot more study.

Yes thanks. For a point to actually occupy a location then it must have a dimension - the minimum being a plank length. Anything less than a plank length is meaningless and can not logically be used to define a point. This length then can be used to calculate pi.

Just a very wild idea. It starts by defining a "point" as being a Plank length (there is some logic behind this idea) and then using this measur the circumference and to calculate pi by dividing the circle into triangles with the plank length on the circumference. A circle with a radius of one plank length has a pi = 3.0. Pi increases as the radius grows –but will it end with a rational number?

Does light experience time? If anything could travel at the speed of light would it experience time? It would seem that photons now arriving at earth from the edge of the universe experience the big bang and then find our earth as it is now with nothing in between. To them it would appear that our world was created in the big bang.