Re: Entropy can be reset to initial or previous state

Silhouette wrote:obsrvr524 wrote:That author points out that people have had a lot of trouble understanding the issues of infinity
I'm sure that I'm not in a position to argue with Euler, Hewitt, Newton, Gödel, Robinson and probably hundreds of others
You seem to have trouble with it all just as the author of that article, Hermoso, admitted to having.
The author of that article I linked, and both you and I aren't in a position to argue with Euler, Hewitt, Newton, Gödel, Robinson and probably hundreds of others too. How about James?
The difference between his usage and the last 70 years of the number set being accepted to the extent that it has been seems striking to me, as does the logic behind his usage. You, James and I may not be world famous mathematicians, but does that mean we are equally amateurish? It's not without problems for each of us to argue the relative legitimacy of our arguments, and regardless even of the full potential that we each achieved at any given point during our respective lives, the standard of what James wrote on his blog some years ago is of the sort I used to play around with when I was a child. Having achieved top marks throughout my mathematical education, and maintaining significant interest and exposure to much higher levels over the decades since, I know there are at least some objective measurements to justify at least a higher level of amateur ability within myself - and I have no interest in overstating this subjectively, but I do have interest in criticising content that appears to me to be exhibiting lower levels of amateur ability, yet is gaining traction and influence over others who may be susceptible to mathematical sophistry due to their own standard being insufficient to see past it. Hell, I might be wrong, but I know there's plenty of reason for me to not be. I will put what I have out there, and you can take it or leave it, though I recommend you take at the very least a healthy amount of skepticism with you that you don't yet appear to be exhibiting.
Why am I thinking that your objections to James are far more about you than him.
Silhouette wrote:obsrvr524 wrote:1) Do you have trouble with the idea that one infinite set can be known to be larger than another?
2) Do you find something specific, very specific, that you consider to be invalid reasoning or usage from James? Please exactly, precisely, quote an example of the error.
1) I have zero trouble with how people can think they understand one "infinite quantity" to be larger than another even though it's undefinable, using their intuitions about finite quantities. The Hyperreals meet the transfer principle with respect to the Reals, but that does not make them equivalent - especially in how to treat their results.
For example, I have zero trouble with representing two infinite sums added together as twice the initial sum, particularly if it is a convergent series. However, to gain meaning from doing the same to divergent series is not without problems that need to be approached with due respect and caution. You can "represent bigger infinities", giving a semblence of size comparison between two or more, but this still makes no real-world sense as they both diverge forever and therefore never get to the point where they can be compared. Any specificity in constructing and comparing infinites is in their means of construction, not in the end itself - which you can only physically get to, by definition, if it's a finite value. Do you have trouble accepting this logic?
So yes, you do have trouble with it. I asked nothing about sums, divergent or otherwise.
And yes, I do see what seems like a gaping hole in your logic. That hole seems to be centered around your inability to comprehend adding to infinity. And then you hold onto the idea that if you cannot understand something, it can only be because the other people are ignorant, amateurish, or childish. I suspect that your protective defense attitude prevents you from growing as quickly as you otherwise might.
Silhouette wrote:2) I've been giving specifics all this time, in particular in this post, which starts off with the most glaring contradiction so far:obsrvr524 wrote:James addressed that issue nicely by first acknowledging what happens when you try to use "infinity" in maths. He explains it doesn't work. He explains that "infinity" is insufficiently defined for mathematical use.metapointperspective.blogspot.com/2014/07/why-universe-exists.html wrote:Using a Cartesian system, there are 3/4 * Pi * infinity^6 points in the entire universe.
But I'm re-reading previous posts of mine as well and they too are specific, exact, precise and with quotes for reference - as you requested... Do you have trouble accepting their logic?
Well okay. That isn't an entirely invalid complaint. But I could easily call it "amateurish" of you. Is that all you have?
Having been a professional observer for years, I can tell you that one of the first things to learn is to not take anything you hear or read too seriously until you have investigated the perspective of the speaker or writer. We called it "linguistic grace". In politics it is the way of conservatives and the opposite of the way of liberals looking for any excuse to express and propagate their hatred.
Probably years before James came to this site, he refused to try to discuss his understanding of the make of the universe with online posters. He expressed two reasons. First he stated that without a good grasp of the infinities, no one is going to understand it. Most people agreed with that idea. Secondly he expressed concern as to what influential people might do with it, especially if they misunderstood it. I see at this site he posted a thread on that issue.
Later on a Catholic site, he attempted a brief tutorial on the general concepts of the cardinality of infinity - how you get from an endless, infinite list to 2 times that list to an endless list of endless lists, "infA^2". He used a story about God calling a meeting of all angels and requiring that his accountant count each and every angel.
My point in mentioning that is that James, knowing that he was talking to people who were certainly not mathematically inclined, spoke to them in simpler terms that perhaps they could more easily understand. It seems that you would have called him childish for using such language. I thought it was smart of him to not use elite sounding verbiage in an attempt to impress them with his brilliance, as you seem to require of people.
In the blog quote that you mentioned, James did use the word "infinity" in a maths formula. Of course, a year prior to that he had explained that in order to use maths properly, you first must rigorously define your "infinity", which he had done as "infA". So why didn't he use his infA notation in that blog?
From James' perspective, a year would have amounted to over 2000 posts on this site discussing both his ontology as well as many other issues. He would have seen his audience as regulars who were probably tired of his explanations. He would have known that this audience knew what he was referring to when he said either "infA" or "infinity". It wouldn't have been an issue. But his blog is a different audience.
You are accustom to interrupting trains of thought for sake of extraneous details. I have observed you doing it greatly in merely the short time that I have been here. Perhaps James knew that such interruptions make it difficult to follow a newly presented idea. So rather than confuse a new audience or further bore the old audience, he said what they all would understand most easily.
People who get pedantic with their language and have no linguistic grace usually don't go far unless they are speaking to an elitist audience of highly educated high brows. I'm sure that James would not have seen this audience that way.
So actually I think he did the right thing by NOT using the "infA" notation in a place that would have just led to more confusion and need of explanation, even if it was technically insufficiently defined enough to impress the non-amateur elites.
If you want to play the game of pedantic, "no linguistic grace", you might find yourself steeped in issues and far less respected than you would have been. Just a very brief example (try not to get carried away) is your use of the phrase "infinite sum".
The term "infinite sum" is an oxymoron. A sum is a finale, end point. Infinite things don't have ends. How stupidly amateurish of you to not know even that elementary detail.
Of course with a slight bit of linguistic grace, I can accept that you were referring to the sum of infinite series'. Although I don't see why you brought up summations of infinite series' since that has nothing to do with the question at hand. An "amateurish" distraction perhaps?
But again, using a touch of grace, it is easy to accept that you were reminded of something very slightly related and chose to get the thought off of your mind without concern of its distraction. An "amateurish" compulsion?
To sum all of this up, what I observe is that you have a problem grasping the idea of adding to an infinite quantity. I surmise that you instinctively feel that you have to add things end to end and thus cannot add anything to something that doesn't have an end. And if you were right about that, not only would Euler, Hewitt, Newton, Gödel, Robinson and probably hundreds of others be wrong, but the entire universe would have to be considered the same size as a 1 inch line segment. Both would have the same number of point locations within.
And that is the problem that I see in your logic.