Entropy can be reset to initial or previous state

Philosophy Forums Science, Technology, and Math
181

I believe I can explain both of these understandings simply as a result of the use of different numeral systems with different bases. I’ll tie it back in with the rest of your post as I go along.
1+1=2 requires a ternary or greater numeral system, usually decimal by human convention in most of the modern day world.
1+1=11 would require a unary numeral system to be true, adapting what would otherwise be “0+0=00” if one were to extrapolate what a base 1 system would look like back through ternary and binary to unary, except 1+1=11 looks more intuitive and meaningful - because using only 0s would make it look like there’s only zero values being dealt with, when the intention here is to be dealing with non-zero quantities. However, it doesn’t actually matter what symbol you use for “1” in a unary system, so long as it’s understood that the symbol being used is equivalent to the quantity “1” in e.g. decimal. “q+q=qq” would even suffice. This is not to be confused with qq representing q*q as it does in conventional algebra. 1+1=11 is simply the result of using the same “carrying” convention that all base numeral systems use: once you exceed the number of symbols for the base you’re using, the next number up resets the unit back to the first symbol and a 1 is carried over to the next position, added to anything that’s already there, if there is anything. In the case of 1+1=11 there isn’t anything there, so the unit 1 is reset and a 1 is carried over to the next position, making “11”. There are other numeral systems of course, like Roman Numerals, but they don’t follow the same conventions - though coincidentally enough I+I=II in just the same way as this unary system that I’m describing. Obviously they change beyond the quantity “3”…

But back to base numeral systems, 2 and 11 are quantitatively equal, just represented in different bases. Quantity is the underlying concept that is being denoted either way, and how you represent quantity is arbitrary, but some ways are easier and/or more appropriate than others depending on the application of the quantity. Binary for open and closed computer circuits is an obvious example. Decimal is just convention that is more or less convenient for everyday mathematics and arises easily from the number of digits on both normal human hands.

This is a side point, obviously, and I hope I’ve explained it clearly enough.
Mathematics has always been easy for me, and it mystifies me too how some people simply cannot grasp it. In a way, we learn like monkeys to think in base ten, when 1+1=11 in unary is just as fine as 1+1=2 in decimal, albeit contrary to convention and with numbers quickly becoming unwieldy as they increase in quantity - compared to higher base numeral systems. Both can be “true” - I think it helps to simply be as “multi-lingual” as possible to understand as many different perspectives on quantity as possible, for the sake of knowing the meaning of what’s going on at all levels of education.

Are we in agreement that number systems simply “refer” to quantities, where the symbols and presentations of the different bases are the “signifiers” and quantity is the “signified”?

This is my understanding of language - in keeping with de Saussure.
Symbols are convenient and distinct shapes that are real visual sensations. Words can take the form of both visual symbols and auditory language.
Less convenient, but equally real things, like trees and cars can simply be associated with these words/symbols: and thus the signified is represented by the signifier. Language comes to be associated with all things, representing all real phenomena in a form that is not what it represents, but is accepted to denote what it represents. This is why languages can vary so hugely across history and geography - it’s essentially arbitrary, the only thing that matters is that it’s socially accepted and useful. You don’t have to physically drive 2 cars up to someone to communicate a quantity of 1+1 cars.

One thing both signifieds and signifiers have in common is that they require bounds/definition in order to apply to something specific. Problems arise when defined finite signifiers are required to give bounds to that which is not definable - or infinite/boundless. What exactly is meant by a finite word when it denotes something that cannot be entirely conceived/grasped/isolated?

I hope you appreciate just how bizarre a notion it is to “define” something that amounts to infinity.
Notice how it’s always necessary to inject something undefinable into any definition of infinite series: for example, [1+1+1+…+1] has this mysterious “…” in it. What exactly is this “…”? It’s not merely 1+1 or 1+1+1, but it’s an instruction to keep adding 1 without bound on how much you do it. “Keep doing this indefinitely” is a definite instruction, but it is a definite instruction to do something an undefinable number of times. Therein is hidden the undefined element of what is otherwise a very precise definition. Even the conventional format contains within it the same mysteriousness: " i=1 ∑₀∞ 1ᵢ " has all these finite terms, but that one infinite term ∞, which is that same instruction to keep adding 1 without bound on how much you do it. Again, for a definite instruction amongst all those other definite symbols, it’s a definition instruction to do something undefinable. That “undefinable element” remains no matter how precise and defined you want to make any “signifier”, as it logically must do when the “signified” is an undefinable. Replacing the (1+1=) “2” with the “11” changes the signifier, as does calling [1+1+1+…+1] by a different symbol infA that hides the “…” mysteriousness just one more layer deeper. The undefinable “signified” will necessarily still be contained within any attempted definition denoted by the “signifier”.

I like this “conflation of map with terrain” wording that you’ve used - it mirrors this signifier and signified terminology that I’m using. The map can take whatever seeming finitude that you want to use, but in defining it as meaning infinite terrain, the definition will necessarily somewhere be hiding or de-emphasising an undefinable somewhere in there - no matter how layered and sandwiched it is amongst finites.

182

Hey watch it, pal. I didn’t ask to be a special needs philosopher… I was born this way.

183

Haha, bro, ur philosophy skills are far better than special needs standard. We all have things we find easier than others, and no doubt there’s plenty of things that I suck at, which mystify others as to how I can be so bad at them.

I’m just fortunate that on this forum, particularly on this topic, things I’m bad at don’t come up :sunglasses: For example, while I might own you on a math test, you’d own me in a public debate in real time - probably even if the debate was math related :confused:

184

oh stop it.

these days i usually rely on my dazzling charisma and fantastic personality to win people over to my side, and in a way this is really cheating. i’ve found that pathos and ethos is far more effective than logos in rhetoric, and so i’ve become a sophist. hey man it works. i keep people up at night thinking about shit… and that’s what it’s about. like fritz, my goal is to make people uncomfortable… to plunge them into an intellectual crisis… to sift the diamonds from the dirt.

i’m trying to save their immortal soul, sil, and it ain’t easy. you gotta come up with all kinds of crafty psychotronic shit to do it.

185

Then you misunderstand the problem being presented.

And all of that reveals the problem.

There are things that are not defined. I don’t believe there is anything that is undefinable. To say that something is undefinable is to say that it cannot ever be understood, that there can never be a description of it, that no word could ever represent it. But if such a thing existed, how could it ever be brought into a conversation?

You are saying that to be infinite or endless is to be undefined or void of description. Yet I just described it. The word “infinite” is a very well known and understood word found in any dictionary.

You explain that because infinity is boundless, there is always something left out of the description such that odd symbols, “…”, must be used to fill the gaps. Yet those symbols are always defined and well understood.

There are no gaps in the understanding of what “infinite” means, the concept. It is well defined in language although insufficiently well defined for use in basic maths. But that doesn’t mean that it is undefinABLE, merely insufficiently defined at the moment.

Explain how a concept can be well understood and often used throughout society and yet be undefinable, forever without description.

Before you say that the concept itself has no bounds, realize that any finite value is outside the bounds of the concept of infinite. It certainly has bounds, The quantity one is outside of the bounds of the concept of infinite. Anything that has an opposite or even a definable difference has a bound or limit.

When James defined infA as [1+1+1+…+1] he was saying that infA is NOT [2+2+2+…+2], which he described a “infB”. He was intentionally putting a limit on it. It was infinite but NOT any and all infinite concepts. InfA was distinguished from other infinite entities - finitely - “well” defined.

You have been conflating a boundless series with a boundless description of the series. And I suspect that I know why. The description has been bounded and complete all along else you couldn’t write it or talk about it. It has been the description of a series that by definition has no end. That is its finite definition. The definition is finite. The word is finite. The concept is finite. The only thing that is not finite is the reality being signified.

If you don’t buy that, please don’t merely repeat your declaration again and again but instead, prove that the concept known as “infinite” cannot be defined, explained, conceptualized, or understood.

186

You’re not wrong that pathos and ethos work, which in itself hides an undercurrent of logos in your method. Is that gonna keep you up at night and plunge you into an intellectual crisis?
As far as rhetoric goes, sticking only to logos is somewhat analogous to restricting your life to the sterilised and sanitised - leaving your immune system vulnerable to attacks of pathos and ethos, which almost all other people are equipping to their tool belt to give them the highest chance of emerging successful. Imagine now, a perverse and somewhat masochistic immune system that thrives from the punishment of holding its own arms behind its back - to mix metaphors even further. I don’t like the dirt, I want to be the diamond - so I revel in the pain of the dirt that others inflict on me just to prove by contrast how sharp and invincible I am, at least to myself. And everyone else can laugh at how I’ve proven nothing, but you gotta entertain yourself somehow right?

I’m sensing a theme here. I still think you’re mistaking misunderstanding for lack of acceptance, but that’s what the logical content of our argument is for - as follows:

Firstly consider the set of all things definable.
You’re saying there are no other sets, or if there are any other sets they are empty?
The latter would be strange, as other sets would by definition be the sets of all things not in sets: a contradiction, yes?
The former is also strange, if it implies that all things are definable - then what is that compared against? You offer “the not yet defined”, making the opposite of finite like the “prefinite”. In doing so you make the possibility of the undefinable undefinable - thus validating its existence through this property.

Negation is an interesting concept. You take a definition and then you say “not that”. Have you then successfully defined everything that isn’t what you initially defined? I find this dubious.
Define the finite: this is fine for me, no contradiction. Then say “not that” - have you then defined the infinite?
I can bring into conversation a not-tree and the meaning you’d extract would exist as a product of the meaning communicated by defining a tree. The meaning understood, after bringing into conversation a “not-tree”, doesn’t come from all the other defined and pre-defined things that exist other than trees. You don’t have to define everything else in the universe just to understand “not-tree”, even if you could and did define everything else in the universe. All that is relevant to the meaning of “not-x” is the meaning of x, and knowing that “not that” excludes it.

To further this line of thinking, it’s possible to bring into conversation black whiteness, upward downness, or square circles. You understand each concept separately, and you understand confusion and/or the concept of one thing not being another. 1 is not 2 - we can discuss this, but this does not validate 1-2ness where 1 is 2. Contradictions can be discussed without them being true.

So being able to bring something into conversation is a poor test to justify logical and/or definitional congruence of the subject matter.
Being able to describe something via negation is not a description of “what isn’t that thing that has been negated”.
As such “…” can be spoken of in conversation, and defining any finites by which it is constituted makes perfect sense. But, for example, if you exactly define “here” and exactly define how to move away from “here”, have you exactly defined where you’ll end up? For all the finites involved in attempting to define “…”, this is where we can specifically define the point after which it goes astray from the defined into the undefinable. Defining the start point of departure from the defined isn’t defining “the departure from being defined” itself, just what’s around its starting point. It’s like saying “count upwards from zero, we’ve defined zero and counting upwards, therefore we know the number we’ll get to if we never stop”.

This is an intriguing inversion. With the infinite being beyond the scope of the finite, the finite can also be thought of as beyond the scope of the infinite?

I’m warey of the possible formal fallacy of Affirming the Consequent worming its way into here: (P => Q, Q) => P, is the reverse true?

Is one really beyond the bounds of the concept of infinity, or is one contained infinitely within the concept of infinity along with infinite quantities of other quantities?
If one was thought to be contained in an infinite set of all finites, then it would not follow that one is outside infinity, whilst it would still be consistent to say that infinity is beyond the finite quantity one.
You have to me careful of how you structure this conception of infinity as different to e.g. one, and as you’ve gathered, I would say you have to be careful of structuring the negation of the structured (the infinite).

James may have intended infA as [1+1+1+…+1] to be NOT “infB” as [2+2+2+…+2], but as you will have picked up, 2 can be represented as “1+1”, making infB [(1+1)+(1+1)+(1+1)+…+(1+1)], and by the associative property of addition infB represents [1+1+1+1+1+1+…+1+1], and since “…” is an endless string of "1+1"s, [1+1+1+1+1+1+…+1+1] is just another representation of [1+1+1+…+1] as implied by “…” - meaning infA is indistinguishable from infB. Note that I am not saying that they are therefore same, succumbing to the fallacy of Affirming the Disjunct. I am saying that one endlessness is not definably different from another endlessness. Again, endlessness is a quality, not a quantity - its quality is that it defies quantity. So intending infA to NOT be infB by attempting a definition of each that “looks” different, doesn’t mean it is different - nor does it mean it’s the same. There is a False Dilemma fallacy to be warey of here, when it comes to the infinite (the endless).

So we’re distinguishing here between the description of infA or [1+1+1+…+1], and the boundless series that they represent. The former describes the latter as boundless. The former has the form of boundedness, the latter has the lack of form of boundlessness. As such you can talk about the bounded appearance of the former without contradiction, and the bounded description is of the boundless, therefore the boundless is defined and bounded? I’m saying that properly scrutinised, the former (the description) when fully unpacked and every element evaluated, in order for it to validly describe boundlessness, there must be at least some element of boundlessness in the description. Otherwise, the description improperly applies to that which it describes. I’m not conflating the two, I’m demanding precision such that they can validly match to prevent any conflation from occurring. To treat the appearance of a description like infA or [1+1+1+…+1] as “defined” and therefore the infinity that it describes as bounded and defined fails to meet up to these precise criteria that I’m demanding. If you don’t accept these demands, as you very well may, all that means is that you’re content to be insufficiently precise in order to force sense where there is insufficient sense upon further scrutiny.

187

That’s why people lie so much.

People get into the US Congress so that they can spend the rest of their lives doing nothing but lying. There are no negative consequences for lying once you’re in the US Congress. Where there are no consequences, fools rush in, very much like the social media, chat programs, and discussion boards.

“Hey why not? It works and without pain.”

Well, I think that’s enough.

I thought it was good that we resolved that language processing was underlying our disagreement. At that point I placed a tiny bit of hope in making progress. Fortunately I didn’t place much hope in it.

I can clearly see now that the map versus terrain issue is merely a symptom of a much deeper language processing problem involving maintaining category integrity. I was dubious about being able to handle the map versus terrain issue. The deeper issue presents no hope at all. I think it is getting just too Sil-ly.

If you could have gone one item at a time as I suggested, we might have been able to get somewhere. But since you insist on these wallpaper posts when you can’t write 3 sentences without at least one being incoherent it is pointless to continue. If you were in the US Congress, everyone would know that it is all just double talk and no one would care.

Besides all of that, I was really only wondering if you had a valid argument against James’ infA theme. I can see that you actually don’t. And as I said, I am no psychologist qualified to handle this kind of language processing issue. And this isn’t a subject of much interest to me anyway. At least now I am pretty sure what it was that James must have felt. I can’t image keeping it going for all day every day for years. He must have had a pretty good reason. He seemed to have had a reason for everything.

I don’t want to get too undiplomatic here (not that I haven’t already) so I think I’m going to have to call it done as far as it’s going to get done.

How do they say it, “we will agree to disagree” or until we find agreement.

The stage is yours. :slight_smile:

188

Oh it’s perfectly coherent.

You just go x = definable, and then “¬x”.

Have I defined “¬x”? No. I’ve defined “x” and then said “not that”. I explained this, but if you can’t read beyond 3 sentences then it’s pointless to continue.

For “E”, the set of all things that exist, the only thing not contained in E is “¬E”.
To make this even clearer, E contains all the things that are ¬(¬E), which includes “¬x”.
Thereby ¬x ∈ E, where E is the set of all things that exist.

To say this is incoherent is to say logic is incoherent.