Where will I find it defined here? I can get the formatting, just not the syntax to activate it. [ TEX ]t_2-t_1[/TEX] or \(\Delta t\)

It isn't really defined here. I take it you mean you want to know how to write equations in TeX? There are lots of intros on the web. If you have a more specific question, ask away.

No. The syntax for equations is elsewhere. What I was asking about was how you invoke them: i.e. [ TEX ][ /TEX ] There's a long delay that occurs before it actually renders, where it looks like it isn't doing anything. I never know whether I've gotten it right until I finally see it rendering correctly. Anyway, I figured it out, as is witnessed above. i.e.: [ TEX ][ /TEX ] (but without the spaces)

Haha. No. Once it has rendered it the first time, it doesn't need to do it again; it stores it with a unique ID. Kind of like web pages are cached so they load faster thereafter.

Kinda like storing information in memory? Don't we cache information in our memories? Don't we have a saying that "once you have learned to ride a bike, you never forget how."?

Not at all. There is no learning here (which involves being able to apply that knowledge more broadly); there is only a simple record of a unique event. That unique recording does not in any way help toward any other task it's asked. Example: You have been told that 1+1=2. For a few days or weeks after this (until that recording is purged), when asked what does 1+1 equal?, you can say '2'! But if asked anything else, such as what does 1+2 equal?, you will have no idea.

I know what you mean and in that respect I agree. However, nature itself seems to know what the answer is without needing to study mathematics. 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, sound familiar? You can find it throughout nature. How does it do that?

You're right and I am sorry, not trying to hijack the thread. The thought just came to mind. Common denominators and such......Please Register or Log in to view the hidden image!

You might be interested in this: http://digg.com/video/why-gold-ratio-irrational The second half is the mathematical demonstration, but the first half shows how/why may of nature's mechanisms can be represented to us by the Fibonacci Sequence. It is simply the flower achieving an optimized seed arrangement. Plants that have a high seed-to-area ratio propagate better than plants that spend too much of their resources arranging too few seeds.

Thank you for that link. I agree and tried to propose (albeit inadequately) that the same phenomenon of "movement in the direction of greatest satisfaction" occurs throughout the universe in the many forms as in the demonstration. I always qualified my posits re the Fibonacci sequence(s) as a naturally occurring mathematical function. A flower does not "need" to know the mathematics, it just evolved to achieve an "optimized seed arrangement", which happens to lie in the FS. If I recall, DNA also follows this efficient structure. Nothing mystical about it. It's one of the ways how the universe sorts itself into recurring patterns for greatest efficiency. IMO, the beauty lies in our ability to discover these naturally forming efficiency patterns (functions) and represent them with our symbolic scientific descriptions as mathematical forms of growth functions, as well as being visually satisfying in the arts.

And hopefully of interest to you. https://www.fq.math.ca/Papers1/55-5/Boman.pdf I just hope I haven't offended anyone with my fascination with these naturally occurring mathematical functions.

One last post. Please Register or Log in to view the hidden image! ...........symbolic art in the fibonacci sequence........ Note its resemblance to the neural memory storing of the brain as described by Dr Hameroff anesthesiologist) In this really interesting presentation, where I saw the Fibonacci sequence in nano-tubulars which he and Penrose believe may be tiny quantum computers. The Pyramid is shown @ 10:50