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 isnât an entirely invalid complaint. But I could easily call it âamateurishâ 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 âlinguistic graceâ. 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, âinfA^2â. 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 âinfinityâ 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 âinfinityâ, which he had done as âinfAâ. So why didnât he use his infA notation in that blog?
From Jamesâ 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 âinfAâ or âinfinityâ. It wouldnât 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 donât go far unless they are speaking to an elitist audience of highly educated high brows. Iâm sure that James would not have seen this audience that way.
So actually I think he did the right thing by NOT using the âinfAâ 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, âno linguistic graceâ, 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 âinfinite sumâ.
The term âinfinite sumâ is an oxymoron. A sum is a finale, end point. Infinite things donât 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 seriesâ. Although I donât see why you brought up summations of infinite seriesâ since that has nothing to do with the question at hand. An âamateurishâ 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 âamateurishâ 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 doesnât 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 doesnât mean that A=B, because B might not be adequate to A.
Like say, a âleft shoeâ is adequate to âshoeâ, but âshoeâ is not adequate to âleft shoeâ.
âAccording to the experts, they are both endless, but not equally endless.â
Yes, according to logicians as well.
James and I understood each other well as logicians not having to show each other our CVâs, 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 doesnât need to refer to his diploma or âexpertsâ but can just argue a case directly.
Depth of infinity.
The infinity of rational numbers is deeper than the infinity of integers.
I honestly have no idea, since logic has nothing to do with the writers. This isnât the only instance of argumentum ad hominem that Iâve seen from you. Here is another:
Again, I understand adding to infinity perfectly - Iâve been trying to explain to you how to do wit all this time. I also understand (I just donât accept) how people are doing it incorrectly, and when they do this it makes them look amateurish whether they are or not: this is not an accusation, itâs just a comparison. As a âprofessional observer for yearsâ, I donât get how itâs passed you by that what Iâm explaining is the legimitate way that all these names youâre dropping either came up with or used themselves - and itâs not how James has been treating infinities. I donât really have an interest in âgrowingâ in my capacity to accept the illogical, so Iâm fine with your suspicion, but thereâs no accounting for taste.
I mean, you should have been? This is my whole point?
This is another argumentum ad hominem: again, the writers (or speakers) have nothing to do with the soundness and validity of the logic being presented. Itâs interesting that you find this fallacy in conservative politics - I do too.
As such, as interested as you are in the history of some poster on this forum, I cannot say the same for myself - again no accounting for taste. But luckily, his past that youâre paying a suspiciously high amount of attention to has nothing to do with the logical content of what heâs said. Not sure where all this devout loyalty and empathy is coming from to just some guy and some things he said - again, whereâs that healthy amount of skepticism that we should apply to all thinkers based on the logic behind what theyâve said? No ill will to the guy, intelligent or not, I donât care - I only care about the logic of what heâs said. Let it be clear that anything Iâve suspected about him has nothing to do with what Iâm making of the logic of his arguments.
Maybe he was dumbing down his language and presentation for the benefit of others, maybe not - again, amateurishness is just a comparison Iâve made and a suspicion I have, which I care not to confirm either way - the content is all I care about.
Whilst I sympathise with trains of thought being interrupted on an emotional level, if the foundations of your tracks are flawed - itâs better on a rational level that this is pointed out before you allow the train to reach its destination, or in some cases even begin its journey at all.
Such flaws may seem extraneous to you, but as a precise and unforgiving thinker, to me, every detail of the foundations must be examined and addressed to ensure what is built on top is sound and valid: another thing Iâd recommend.
Try building computer programs with a missing piece of punctuation, some faulty logic, or a missed logical condition. If it compiles at all, it will be buggy.
Maybe this is only the realm of the highest level of thinking, and maybe this isnât how James saw his audience, but either way I perhaps have a different approach to rigor, about which I attempt to be as clear as possible. Gaining respect is not my concern, I have no emotional investment, I just contribute what I feel ought to be contributed for the sake of illuminating flaws and improving thinking.
Feel free to read the first line of this section of the wiki article as I comment on the irony of your accusation.
Perhaps you misread me, but what youâre saying here was exactly my point in the first place? That infinities donât have ends and they are a means of construction to represent the tendency towards the infinity that you never get to. An infinite sum is a construction to represent this as an infinite series.
I wonât accuse you of being amateurish for making a simple mistake in your reading, but I will express concern over how exactly wrong you were in reading what I wrote:
Infinite series have everything to do with Jamesâs use of infinities, as this is how you mathematically operate on hyperreals, as he attempted to do. This is how you move away from an amateurish way of treating them.
All these names are just fine with the treatment of infinities as I am explaining - they treated them the same.
Honestly, I donât think this discussion is going anywhere. I understand youâre invested in defending this guy for whatever reason, Iâm just trying to help. Clearly you donât want it, and I donât want to bother you with it if you donât want it.
I assume you mean âSufficientâ? I guess theyâre similar in meaning and maybe itâs a translation thing, but just so you know, I believe the English convention is to use the term âSufficientâ. This is probably why obsrvr524 didnât know what you meant.
By definition no, since a line represents 1d space.
I assume this is your basis for the concept in your next post:
But the distinction between a line and volume is irrelevant to the infinitude of either, because the information contained along an infinite line can also be represented in 3 dimensions.
Your argument would appear to be that the form of the representation of infinity affects the âquantityâ of the infinity, for which youâre using the term âdepthâ - but comparing depths implies comparing quantities.
Theyâre both representations of that which has no bound and therefore canât be defined. As Iâve been explaining to obsrvr and as you probably already know, finitude is the derivational root of the terms âfiniteâ and âdefineâ, meaning bounded. You can define finites, and you can represent the tendency towards the infinite through constructions that specify finites (infinite series), but strictly logically thatâs the closest you can get to âdefiningâ infinites such that you can compare them. But one definition of a divergent series that tends to infinity has no bound just the same as a definition of a different divergent series - thereâs no final bound either way to compare the final result. All you can compare is the construction that uses finites. As such you can manipulate and perform arithmetic on the constructions because they use finites, but the final result is undefined whatever construction you use to represent a divergent series.
The difference in âdepthâ is in the representation, not in the result.
Even though this escapes obsrvr, perhaps you understand this?
As I explained to obsrvr, it doesnât have an echo, nor does it need an echo.
Entropy is non-linear, as demonstrated by the equation for change in entropy: ÎS = â«ââ ÎŽQ/T.
The higher the ÎŽQ (difference in energy), the higher the ÎS (change in entropy) - a proportional relationship - and as spacetime uncurves and the constant energy of the system spreads out, thereâs overall less and less differences between points of higher and lower energy, meaning thereâs less and less change in entropy. In short, the rate of entropy increase slows down: therefore itâs not linear.
But the equation also shows that the higher the temperatures involved, the lower the change in entropy (they are inversely proportional, hence the T being on the denominator). So areas of high temperature gain entropy slower - which might give the impression of entropy being constant, or even resetting itself (echoing back on itself) when the temperatures are really high - such as in stars and black holes. But overall the entropy still increases, just slower (again, not linear).
It seems to me that if the universe has always existed and the universe is infinite in size, the average entropy level for the universe as a whole could never change. For every location where the entropy is increasing there must be a location where the entropy is decreasing. I donât see any way around that.
And it probably never stays the exact same in any one place.
Interesting that the term âadequateâ exposes so much literacy problems. A good indication of why it is so difficult to argue with âexpertsâ.
Indeed. A line is 1 dimension.
No. It could be construed that way, with some effort, but thats not very elegant.
In fact the definition occurs at the formulation, at the outset.
Thats what the key to Jamesâ calculations is. Work with the formulation, not with the results.
That goes for âinfinityâ in general. There is no âresultâ.
Oh shut up you tool. Seriously. Donât tell me to be impressed by someone who can recite the ABC.
I had a solid background in theoretical physics when I was 8. Fuck off.
Actually Silhouette, what you said is wrong, or my saying it could be construed that way was wrong -
what I mean with a deeper infinity is one which expands quicker. The rate of adding up is greater with a deeper infinity. Why does this matter?
It matters because this is how James arrives at the idea that space is âlargerâ than time and cant be reduced to it, thus why there is no cyclical universe, no eternal recurrence of the same.
Letâs look at this âprecise definitionâ:
infA = (1+1+1+âŠ+1)
Now to perform some arithmetic:
infA ^ 2 = (1+1+1+âŠ+1) * (1+1+1+âŠ+1)
Time to sequentially multiply the terms as you do for multiplication of values in parentheses, letâs seeâŠ
11 = 1, ok. 11 = 1 as well, letâs keep going and what do we get?
(1+1+1+âŠ+1) * (1+1+1+âŠ+1) = (1+1+1+âŠ+1) infA ^ 2 = infA, huhâŠ
Now, letâs compare this with infA * 2:
(1+1+1+âŠ+1) + (1+1+1+âŠ+1)
But instead of putting one after the other like you would normally do for addition of finites (which the very formulation of â(1+1+1+âŠ+1)â tries to do in the first place!!), which would get âinfAâ just the same as if you multiply them, letâs remember there is no end to add the next term to, and sequentially add the terms the same as you do for multiplication:
1+1 = 2, ok. 1+1 = 2 as well, letâs keep going and what do we get?
(1+1+1+âŠ+1) + (1+1+1+âŠ+1) = (2+2+2+âŠ+2) infA + infA = 2 * infA
Ooo, have we got somewhere? Letâs check against the rule: âx^2 > 2xâ iff âx > 2â
Ok, so âinfA > 2â check.
Therefore infA^2 should be âlargerâ (deeper?) than infA2
Recall:
âinfA * infAâ was âinfAâ and âinfA + infAâ was â2 * infAâ, wait what?
Our results show infA^2 < infA2âŠ, which would only be true if infA was less than 2âŠ
(1+1+1+âŠ+1) < 2? NopeâŠ
Looks like even being able to recite your ABCs and using the secret of Jamesâ calculations and working with the formulations is a good start to being able to see how it makes absolutely no sense whatsoever.
Yes, beautiful, Silhouette literally comes out proudly demonstrating that he knows how to make 1+1 add up to 2, and Promethean is actually impressed. Probably thinks it is relevant to my point about different orders of infinity. Go ILP.
James adds 1s together with â(1+1+1+âŠ+1) = infAâ and everyone loses their minds over his genius that inspires readership and ideas in others, or makes others want to compare their own ideas to his.
Sil unproudly shows it falls apart at its most basic level and is ridiculed for actually doing the arithmetic at its most basic level to prove it.
Go ILP indeed.
Thereâs no point in anyone staying anyway because nobody ever wants to learn anything.
Make claims, ridicule counter-claims, flatter self and either leave or repeat.
Letâs have a look at âdepthâ and prove what Iâve just said as well:
âExpands quickerâ/ârate of adding up is greaterâ
This assumes a finite time taken to add up each element in constructing the infinity, and an equal time taken to add up each element for each construction of infinity.
Otherwise adding up (1+1+1+âŠ+1) twice as fast as (2+2+2+âŠ+2) makes each âexpand at the same rateâ and the ârate of adding up is the sameâ.
Either that or donât assume a finite time taken to add up each element, and instead add each up equally instantaneously â âexpand at the same rateâ and the ârate of adding up is the sameâ.
Ergo different depths/orders of infinity argument is unjustified yet again.
Destroying ILP arguments is too easy, but getting people to listen and accept, nevermind learn and grow is impossible.
But at least he took your advice, promethean, and got out while he could - well a bit late.
At this point, I have to accept that Silhouette is just being the anti-James political pundit reminiscent of Juan on Foxâs The Five, the paid-to-be anti-Trump pundit for the show. Juan ends up making such ridiculous and stupid arguments that no one can believe that even he believes what he spouts even though he does deliver it as though perfectly serious.
Sometimes it is really difficult to tell if pundits just believe that their audience is stupid, as US democrats seem to believe, or whether they really are that stupid themselves. Perhaps they are just trying to gather up all of the really stupid people for future purposes.
I wonât bother to play into the game of pointing out obvious reasoning errors with someone apparently just making dumb arguments for sake of hating on the other guy. Whether political or just stupid, such people only learn in private, when at all.