studiot

I know this is for an essay, But I think it is legitimate to ask your questions in the main relativity section. Homework help requires you to show your working here, which is not appropriate at your level. So ask (send them a private message) a moderator to move this for you. There are some really good folks here with great knowledge of relativity. I don't know how what your timescale is but this book could have been written for you. My local public library has a copy. Note that Special Relativity is founded on two principles General Relaticvity introduces a third principle and also the Einstein Field Equations. Note the plural - there are 10 of them, usually rolled into one big one that you will not yet have the maths to work. Go well with the writing, and tell us the timescale.

How does one collate a double limit with an infinitesimal?

That would be good if I could find it. I looked but could only find extracts in pdf.

I have ordered the two books you listed, thank you for the references. It will be interesting to see what they ahve to say. This book is hundreds of £ and out of my means, but I am pursuing a loan copy from our inter library loans system. Then would they also be infintessimals? I rather think it is the other way round. The limiting process can be usefully applied to Infinitesimals. However I think that the OP question can be answered as follows. Limits are the result of the limiting process. Infinitesimals are specially constructed abstract objects, ouside the normal number systems so no, they are not the same. The limiting process has wider applications than differentiation/integration but that is not the subject of the OP (for instance the relationship to asymptotes), so we should explore this in a new thread if you wish to take it further. There are huge and widespread applications in engineering and theoretical physics (relativity).

Asymptotes can be limits.

Only part of it.

What does that have to do with the OP question? Why can we not apply Science to look into any proposition we choose?

In what way? What are you thinking about?

I don't seem to have had an answer to this post I don't agree with this. Examples from statistics come to mind. Whilst I liked the style and presentation of your paper, I don't endorse everything in it. A further comment One thing you don't seem to have examined is the clear difference between infinitesimals and limits. Limits allows one to step over the process of accounting for an infinity of terms, which you correctly say begs the question of do the ignored terms add up to something significant, and go directly the an end result, or show that there isn't one. Convergence theory is all about this. I do not know of any equivalent process with infinitesimals, NSA notwithstanding.

The eco (furniture) factory described in the book is still going strong. https://grimshaw.global/projects/herman-miller-factory/

I agree with this, unfortunately those promoting these shifts tend to be less well resourced and less articulate than the establishment. For example the small book 'Cradle to Cradle' by Braungart and McDonough Is very well reasearched, and contains some excellent examples of actual (successful) cases. However it is very hard to read as its style is not coherent or progressive. When our back have been to the wall (eg WW II) coherent (joined up) Government did indeed lead and direct a successful collective response to an emergency. But real and imminent emergencies do appear to be the only drver for such action. In the Netherlands (Holland) last year the banned the use of gas in new homes. The UK government is considering a similar ban. But another part of the UK government is still offering grant suport and promoting gas boilers. Worse the UK government has fragmented its policy to provide a relaible and stable electricity alternative.

Thank you for the reply Wasn't there a question in the title?

Many think that there are multiple environmental crises assailing the planet. Here is an article on a fresh report from the https://www.ippr.org/, by the BBC https://www.ippr.org/ The degradagation of arable land is cited in the New Scientist book https://www.amazon.co.uk/dp/1473629772/ref=asc_df_147362977258469057/?tag=googshopuk-21&creative=22110&creativeASIN=1473629772&linkCode=df0&hvadid=310865071345&hvpos=1o1&hvnetw=g&hvrand=18039469306525565984&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=1007149&hvtargid=pla-563590850360&th=1&psc=1

I don't agree with this. Examples from statistics come to mind. Whilst I liked the style and presentation of your paper, I don't endorse everything in it.

Takazu Seki, pioneer Japanese mathematician, accountant and chief of the National Bureau of Supply b.early 1640s Edo or Huzioka, d. 1708 We had a long discussion about this subject in a recent thread. https://www.scienceforums.net/topic/116421-definition-of-derivative/?page=3 Many of the references I referred to in my first post here appeared there. You do not seem to have heard of at least some of these.

You have references to this? In discussing the OP paper (the purpose of this thread) I note a psarsity of references to Newton and his input compared to that of Leibnitz and the continentals. This bias towards one or the other european originator is common in articles. It is also common to entirely fail to mention Seki.

Compared to the usual rambling rants against the establisment this paper was clean and tight, with good references. All in all a worthwhile addition to the knowledgebase on this subject and a reminder that no subject is static and that fashions come and go, even in Mathematics. A pleasure to read, I did not know there was/is a movement to re-examine the history of this subject in the light of modern thinking and I can personally vouchsafe the value and veracity of your opening sentence in most disciplines. Nor it seems did wtf. My library goes back to the earlier period you speak of , so I will be comparing some of the texts from that time So welcome and +1 for introducing an interesting subject.

Energy is a property not a thing. The 'thing' theory of energy (caloric) was disproved centuries ago. Exactly so. Space on its own is a general term for the stage where stuff happens. We need to tie it down with qualifiers to properly identify which stage we are talking about. This is why, for instance, my comment used the term free space. But 'Space' could be limited to area or even a linear measurement, rather than volume. Which brings in measure. Many useful spaces (including all geometric spaces) possess a measure or distance property as mathematically defined and called a metric. Unfortunately Physics has (once again) a different definition of the word metric, but it is equally important, especially when considering Relativity questions. Back to the mathematical definiton leads us to consider those spaces without a metric. These are topological spaces and non metric topological spaces lead us directly to wormholes with the 'gluing' rules of topology. Computer programmers use another such space with packman type games on screen. To understand Space and its qualifiers we need to look into set theory, functions, mappings and containers. A good simple example of this would be to explore this view of 'vectors'; this readily shows how you need a 'container' filled with several different sets to develop useful a useful theory - that of vector spaces.

I think that simply saying space is volume merely replaces one word with another. You could equally ask "What is volume?" In fact space is not just any old volume, it is a particular sort of volume. So to say something more useful than "space is volume you" have to detail its particulars. Furthermore that particular volume does indeed interact with energy (in the form of EM waves since there is no such thing as 'pure energy') as evidenced by the easily measurable complex impedance of free space, usually denoted by the symbol Zo.

That about says all that needs to be said. It is clear that there is only one poster expounding inflexible views, regardless of anything anyone else says. I thought it all sounded familiar. Thank you for preventing any further waste of my time. +1

Reg You have pitted direct quotes from one member against those of another using misrepresentation of the words of a third member. Polysemy? I give and gave you credit for stating your definition of mainstream. But you have no basis whatsoever for asserting that 'everyone else' uses this definition. In fact I specifically ruled out any polysemy by the words "in this context" Since you wish to claim that everybody else uses your definition (quite reasonable in some very limited contexts) here is my version. By far the greatest majority of the activities of scientists is in the application of existing Science, not the search for new Science. As such I would offer mainstream to represent the major activity of Science. Application is, by definition, using science for something we want to work and be successful. As an example, since you are fond of these, consider the motor car. There is an existing world land speed record. New Science would be trying to build a car to exceed this speed. But this would be one single solitary car. Set that against the output of the world car manufacturing industry building mainstream cars, using mainstream Science. Turning the the other member statement you placed in opposition brings us to the meaning of "all the time" It may have been an unfortunate use of words fo those who can only take pedantically literally what others say. I did not, anymore than when I use the phrase "I am forever making typing errors" do I mean literally that every word I type is in error or that I will live forever or that I am doing nothing else with my time. You use literary hyperbole liberally and I take Phi's words in the same vain. Most of the activity of Scientists is, as I already mentioned, spent performing activity where it is undersirable to challenge what is known to work. But some of it is spent on new Science. For instance I am reading an interesting book about the history of Earth interior geophysics. In the last two decades our knowledge and understanding of the interior of the Earth has been turned on its head at least 3 times. Perovskite, post perovskite and other matters. Fascinating.

... to which Phi for All responded... I'll probably not win any friends by saying this, but I'd say Sam is, on this point at least, largely right, and Phi largely wrong -- with no disrespect intended to any of our members. Before you can build an argument based on these quotes you have to agree the meaning of the word mainstream in this context. By your own admission, another member introduced the word. So clearly according to the rules of proper debate and argument the onus is upon you to demonstrate that your definition coincides with that of Sam Cogar. That there is more than one possible interpretation of Sam's utterance is demonstrated by the fact that I have a different definition (and therefore understanding of what he said) for yourself. Equally I have a different understanding of PhisforAll's utterance from the one you are portraying. In both cases I may be right or wrong as to my understanding, as may you. So over to you to demonstrate that you have chosen the correct interpretations of the words.

Gosh Reg, the Internet has provided a big boost for the challenging of Science. What do you think of this?

You brought in Mathematics and also determinism and statistics You further made another distinction between determinism and statistics additional to the one presented as (i) and (ii), where they were lumped together. Since they are your creatures can you tell me if a probability of 1 (statistics) implies certainty (determinism) and if you still draw this distinction?

Oliver Heaviside at a Royal Society Dinner, when the famous mathematicians of the day refused to accept his operational calculus because his proofs were not up to their standards.