You can tell the amateurish level of mathematics that we’re dealing with by its presentation.
He’s brazenly multiplying infinities all over the place. What do you get when you multiply, or perform any arithmetical operation on something that’s undefined? Something that’s undefined. Even adding 1 to quantity that has no bound still has no bound - his is the realm where you can make mathematical nonsense such as 0=1. E.g. “Infinity + 1 = Infinity, subtract infinity from both sites of the equation and bam” - that’s what you get when you treat infinity like a finite quantity.
You can sum up what you’ve quoted of him in a couple of lines:
Conventionally we use 3 dimensions to measure space and 1 dimension to measure time, therefore space is bigger than time.
There’s more ways to be heterogenous than homogenous, therefore heterogeneity is more likely i.e. everything being the same has lower entropy than everything not being the same.
The first line says nothing, and the second line just says “entropy”.
So I take it back, you can sum up all that nonsense in one word: “entropy”. There’s no need to make a fool out of yourself just to explain what one word already explains.
Yeah and tell James to stop brazenly multiplying infinities all over the place, too! Fucking affectance ontologists. They’re almost as bad as value ontologists.
Speaking of one who should look things up before posting.
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. Then he gives infA precise definition.
(I finally got that link thing working )
In short, it appears that James knew what he was talking about.
3/4 * Pi * infinity^6 is just as infinite as merely saying “infinity”. And as I covered, multiplying however many indetermined quantities gives you an indetermined quantity.
He’s defined infA the same as you would define infinity, just in an amateur format.
Admittedly writing in unicode for posts here is limited as far as I can work it, but something similar to the following (where i=1 should be below the sigma, and ∞ above) is how you represent how he presented his infA - in terms of an infinite sum:
i=1 ∞∑ 1ᵢ
Yet this is the same as representing infinity. Swapping the term out for “infA” does nothing.
He then goes on to treat infinity algebraically like a finite quantity, and then performs some more algebra to represent a logical tautology…
Next is an attempt to vitiate actual definitions that you use at all levels of education as merely elementary education, as his best attempt to legitimise what looks like a merely elementary education of his own - presumably to make it seem as though there’s no point wasting your time with actually learning higher education, which would not incidentally reveal the nonsense behind his formulations, and potentially draw in amateur level mathematicians to his sophistry, who never wanted to get into higher education in the first place.
“infinity / infinity = indeterminate” is not like saying “length / length = indeterminate”.
Length is a unit, and letting the numerator be x and the demoninator be y, you get x/y, which is determined in that form. Dividing one length by another just means the result has no units, not that it has “indetermined” units: it is determined as having no units.
Then he finishes off your first quote with a conclusion based on his invalid premises.
The second quote is more of the same infinity-algebra, pretending that things like an indeterminable quantity + 1 can be determined with precision, like you would do with determined quantities.
Of course he’s right, the number of real numbers is greater than the numbers of integers, even though of both there are infinitely many.
In the same way an unlimited three dimensional space is greater than an infinite line.
I like the argument that time is smaller than space, but I am not sure what is meant by the universe as consisting of all possible states. Except if all possible states means all necessary states. Possible states would comprise a meta universe that is never fully attained.
Entropy can be reset to initial or previous state ?
Initial or original - appears here that this needs a real distinction. There may not be one, or even, it may not even necessitate a proof for one. That is the first introduced fallacy.
Second, states are a continuum. Prior states are infinitely divisible, and correspond to particular variables. Passing over this leads to a circularity with which to argue space/time is invalid. Invalidity and boundary problems are relativistic .
The reduction will appear in 3 forms , then, phenomenological, eidectic - ontological, and entropycal , - all part of the continuum modally. - changing timespace in terms of preception, understanding and representation.
At that point visualizing absolute space/time will not become feasable.with the problem approaching irresolutability.
That it is so embedded, is the problem.
Other way- absolute, and infinitely regressed fallibility. They may become obsolete by definition, including mathematical ones.
Also entropy isn’t technically a state because A=A doesn’t apply to it.
Entropy means the absence of order, not a particular constellation of disorder, which would be a weird thing.
The laws of thermodynamics presuppose order, where heat as well as heath death are derivates of it.
Existence isn’t actually of an expansive but rather a contracting nature.
The question James’ work first of all evokes, is how there can be different qualities of infinitesimals?
Which actually addresses the deeper question of how one could compute one infinitesimal with another if they have no distinct features. So we do this by using different orders of infinity.
An infinitesimal of the rational order is smaller than one of the integer order. It is the noise within the noise.
I don’t know if there is an infinite number of classes of infinity, but I don’t think so. So thats a start.
I prefer to give an infinitesimal a quality of affect - namely, valuing. Which draws it out of strict analytical infinitesimally - it just has no size or mass requirement to it, it is a minimal concept of a being rather than a concept of a minimal being.
For something to affect it must also be affected. Resistance.
In the end resistance, or friction, is the real cauldron of logical being.
You haven’t impressed me as someone who should be spouting accusations of amateurishness.
Apparently the hyperreal maths which address this exact issue were formalized professionally back in 1948. I image James had plenty of time to read about them and probably before you or I were born.
I might look into that “value ontology” someday but one ontology at a time (I’m still not even comfortable with that word). And at my current pace this could take years just to catch up with James’ posts. I barely have any more time to read them than the pace at which he apparently was writing them. And then there is all of the parsing, categorizing and so on. My parsing program didn’t like the downloaded file from this server. I have a friend who might get around to fixing something for me (someday).
I think the issue was merely tying down exactly what was meant by a chosen infinity, such as the whole number set. And then the math is merely adding to or multiplying that set. The issue seem to be simply that if you have two identical whole number sets (perhaps in two different languages) then you have twice as many as merely one whole number set:
infA + infA = 2 * infA
I really don’t see the complication with it.
With infinitesimals, it would be the same excepting using only the real numbers that are less than 1. He proposed that one infinetisimal = 1/infA. I started to go try to verify that with professional maths but immediately realized that he is the one declaring the definitions, so obviously he is right about them.
The significance of the type of infinity is in the density of coordinates.
This density is lesser in the integer set than it is in the real numbers set.
It doesn’t matter if you multiply the set of infinite integers, the density of coordinates doesn’t increase. Whereas if you take an infinity of one of the more branched sets, you get a higher density and a deeper infinity.
Oh yes, the hyperreals are a legitimate number set, but that doesn’t mean you can just do whatever you want with them and expect it to be valid.
There’s plenty of introductory material on the subject floating around on the internet, but actual examples of their proper use seems to be sparse.
Most of the actual usage of hyperreals in arithmetic seems to be done through sets, for example here where every term in the set is operated on sequentially with the corresponding term in the second set. So it would be legitimate to represent a specific divergent series within a set, and operate mathematically upon that. Dealing with specific infinite series (tending to infinity) is done all the time and is fine.
Other usage seems to be in conjunction with sets of numbers like the real numbers, in order to get a real number result. Concepts like ‘dx’ are used all the time in calculus, which is fine because they represent a tendency towards infinites.
James may have been perfectly aquainted with their usage at the time he wrote what you quoted, but none of it shows. He said he had his “own proof” so apparently intentionally deviated from the legitimate pathway, and what he came up with is extremely dubious.
You say you don’t see the complication with infA + infA = 2 * infA because you’re using your intuitions about finite quantities. Infinities easily result in nonsense and have to be dealt with very carefully.
I’m hearing things like “densities” in posts on this thread, but it doesn’t matter how relatively closer numbers are when they’re added to infinity, for example, the sum is still divergent and not-finite i.e. can’t be defined. It goes on forever so never reaches a point at which it can be compared with another way of going on forever, such that one can be called “bigger” than another. Size presupposes finitude: something “infinitely big” has no bounds to compare to anything else - it can’t even be ascertained to be a specific thing. The only thing it can be ascertained to be is a set of smaller things - maybe even a specific infinite series, which like I said is fine. Care is needed.
That author points out that people have had a lot of trouble understanding the issues of infinity to the point of banning them from professional maths only to have to put them back in later.
I’m sure that I’m not in a position to argue with Euler, Hewitt, Newton, Gödel, Robinson and probably hundreds of others who James seemed to have agreed with. You seem to have trouble with it all just as the author of that article, Hermoso, admitted to having. I wouldn’t be able to competently take up the argument between you and them. But I do have a couple of questions for you.
Do you have trouble with the idea that one infinite set can be known to be larger than another?
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.
James only believed in a six dimensional reality, I never saw him attempt a proof for this.
Personally, I think there is a ‘divine’ sequence that orders the reals in 1:1 correspondence.
An algorithm that is infinitely chaotic won’t formulate an expansion, it’d be indecipherable… I could make a very long post to show this, that you can’t prove higher orders of infinity. Maybe I’ll have the energy later.
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.
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?
I’ve been giving specifics all this time, in particular in this post, which starts off with the most glaring contradiction so far:
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?
Why am I thinking that your objections to James are far more about you than him.
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.
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.
If A is adequate to B, it means we can say that A is B.
It doesn’t mean that A=B, because B might not be adequate to A.
Like say, a “left shoe” is adequate to “shoe”, but “shoe” is not adequate to “left shoe”.
“According to the experts, they are both endless, but not equally endless.”
Yes, according to logicians as well.
James and I understood each other well as logicians not having to show each other our CV’s, but sufficing with our logic.
Even if James never bragged about his credentials and IQ, you can be sure that he, just as I, always scored at the top percentile of any significant intelligence tests. Because he is intelligent, he doesn’t need to refer to his diploma or “experts” but can just argue a case directly.
Depth of infinity.
The infinity of rational numbers is deeper than the infinity of integers.
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