Total posts: 184
Posted in:
This is Norman Wildberger's personal website where he expresses his unusual opinions: https://njwildberger.com/
There is a lot to unpack here, so I'll highlight a few important things:
- Debate with Daniel Rubin: He links to this on the homepage of his website. Rubin was incredibly respectful of Wildberger's ideas, ideas which I suspect most mathematicians would dismiss as nonsense pretty quickly. I appreciate that Rubin was willing to do this, because while I do not agree with Wildberger, it only grants more credibility to conspiratorial quacks when they are ignored by experts. One issue with this "debate", however, is that Rubin gave Wildberger most of the talking time and did not push back very much. He did, however, outline his objections more clearly in another video, which Wildberger neglected to link to or mention on his website. (At least that I could find. Feel free to correct me on this.) It can be found at this link: https://www.youtube.com/watch?v=GnepxZ-ZZOI
- Modern math compared to religion: Wildberger asserts that modern math is in some sense religious, believing in things on the grounds of faith alone. I might respect his objections a bit more if he didn't do this, since many of his other objections are at least understandable, but this assertion that mathematicians so desperately want their beliefs to be true, and that they don't have any real arguments is absurd, and potentially harmful. The assertion is baseless, and it paints mathematicians as complete fools, rather than the geniuses that many of them are.
- Conspiratorial wording: Wildberger uses a lot of conspiratorial wording such as "delusion" and "blindly accept." In this way, he appeals to people who are conspiratorially minded, and who want to feel like they are smarter than the experts. This idea of a widespread delusion is simply nonsense. Mathematicians do not blindly accept statements such as "...and then taking this to infinity..." and they frequently question the meaning of this sort of statement when applied to a context in which it has no formal definition or where its application cannot be justified. They don't simply search for evidence which agrees with their preconceived notions (as Wildberger would suggest) either. Take, for example this paper: https://vixra.org/pdf/1208.0009v4.pdf. A mathematician as described by Wildberger would blindly accept its conclusions, nodding their heads every time "as n goes to infinity" is mentioned. In the real world, however, any credible source will tell you that the problems that this article claims to solve remain unsolved. This is because a real mathematicians questions the use of limits in this paper, and recognizes it as invalid.
- The impact of Wildberger's conspiratorial wording: This is what really caused me to lose any remaining respect I had for Wildberger. Many of his followers hold the belief that modern math is a complete waste of time that does nothing for society. A trip to fantasy land that mathematicians get paid to take. This is problematic for two reasons. Firstly, it makes it seem as though mathematicians don't actually do anything, negating the sheer amount of work and effort that math takes. Secondly, it has lead many of his followers to believe that if mathematicians could only wake up, our technology would be drastically better, and millions of lives could be saved. (One look at the comments on one of his posts reveals just how many of them believe all of these things.) The irony in this is that without the concepts that Wildberger rejects, he wouldn't be making these blog posts on a computer, nor would we understand nearly anything of what we do today about the universe. Switching to Wildberger's ultrafinist math would kill, not save millions.
- "Are mathematicians scientists?": The short answer is no. They aren't supposed to be. Science uses inductive reasoning. Math uses deductive reasoning. Science can change with new evidence. Math is not evidence based, and proofs are set in stone. Science uses experimentation to draw conclusions. Math uses abstract deductive proofs. Science is observation based. Math is done in the abstract, and you can't observe abstract objects in the same way that you can observe physical ones. According to Wildberger, however, the approach of science is the only valid one. This completely misses the point of math, which brings us to my next point.
- Model vs. match: Mathematicians do not assert their axioms as objective truths. Math is not intended to be part of the physical world. Math, like any field of study, should be judged by its usefulness, regardless of how that usefulness arises. Math allows us to model things in reality, but it is not itself part of physical reality. It is a model, not a match, and that is the way it is supposed to be. This is because the physical world can be somewhat of an enigma. In theory, we shouldn't be able to make any predictions at all, because we don't know, for example, that just because F = ma this one time, that F will equal ma the next time we apply force to an object. The equation "F = ma" wasn't found in some deep dark cave signed "Creator of the Universe," we just observed that this equation is consistent with our observations. This is the beauty of math: Our mathematical models can make predictions about something without us actually needing to see it. That is why math is not observation based. Because that would defeat the purpose. Sure, the fact that math exists separately from the physical world means that it doesn't always match the physical world, but that is okay. No one is claiming that everything in math has a counterpart in reality.
- The law of (logical) honesty: Wildberger's law of honesty is a good one. The issue is that it is a moral principle, not a logical one. Not pretending to do something you can't is good life advice, but for the sake of logic, considering theoreticals is incredibly important and useful, and there is no problem with it. Wildberger says that this law of honesty invalidates a question such as "If you could jump to the moon, would it hurt?" I have no issue answering this question: Yes, it would. In fact, you would definitely die. You would accelerate incredibly quickly through the earth's atmosphere and into space, and if you weren't already dead, you would find yourself in the vacuum of space where your blood would boil. Wildberger would suggest that this wouldn't happen, because no one can jump to the moon anyway. My response to this is that it is possible to talk about what would happen if one were to jump to the moon, even if that won't happen. Why is it important to be able to use theoreticals though? No one really cares about what would happen if they could jump to the moon, but considering theoreticals can be very important. Wildberger agrees that it has been proven that there is no rational number equal to the square-root of 2. What exactly is this proof? Well, feel free to look it up if you want the details, but to summarize, it begins by assuming that the square-root of 2 can be written as a fraction, and demonstrates that this leads to a logical contradiction. That's right, we are not only imagining that we can do something that we can't, but we are using that assumption to prove that we can't by showing that it leads to a logical contradiction. It is undeniable that if the assumption that something can be done leads to a logical contradiction, it cannot be done, and yet under Wildberger's "law of honesty" (at least as he applies it) this sort of proof by contradiction is invalid.
Obviously, this does not address everything that Wildberger has to say, as he has said a lot, so if there is something specific that you want me to address, feel free to point it out.
Created:
Posted in:
ChatGPT is weirdly bad at math. It can't even solve a cubic. Problems that take me 60 seconds it claims are impossible. I also managed to convince it that 2πi=0. I guess it is designed for creative writing. It doesn't really have any strict logical principles.
Created:
Posted in:
-->
@Best.Korea
Yes, its all about way of thinking while things are not too bad.
You are right that you will need more than a way of thinking to get through the toughest of times. As you can hopefully see, these 5 points, especially numbers 4 and 5, propose an active approach, not a passive one. We cannot overcome hardship by thinking about it really hard and deciding that we are not technically suffering because something something philosophy. I'm not saying that.
Now, when things are too bad, nothing will save you. [...] In fact, the amount of pain you can feel is almost unlimited. It is limited only by how long you live.
Pain does not necessarily imply suffering, (https://www.sciencedirect.com/science/article/pii/S0149763421003560#:~:text=One%20may%20have%20pain(fullness,%2C%20frustration%2C%20anxiety%20and%20depression.) and I would argue that these points can allow a person to handle pain in a way that minimizes suffering.
Just remember that human being is not capable of always being happy, but is capable of being in pain for years or decades.
Happiness and lack of suffering are two different things. I am not claiming it is possible to always be happy. In fact, I am not even suggesting that one can necessarily avoid suffering entirely. I know I titled this "how to live a happy life in 118 words," but I didn't intend that to be taken too literally. The 5 points themselves are the important thing.
Created:
Posted in:
- Suffering is that which one is inclined to avoid. It is subjective, and varies based on a person's preferences and attitude.
- By embracing suffering and accepting it as a challenge, we eliminate suffering.
- Meaning is subjective and not inherent, but by rebelling against the meaningless suffering of our lives, we create our own meaning.
- Every situation is just another opportunity. We should not dwell on past mistakes, but rather consider them a part of the challenge, opportunity, and meaning of our current situation.
- We cannot always succeed, so we must instead accept that the reason we try, even in the most dire situations, is not for the sake of success, but for the sake of the attempt itself.
The above is a concept for a life philosophy with roots in Absurdism, Optimistic Nihilism, and even somewhat Buddhism. I'm interested to hear your thoughts.
Created:
Posted in:
-->
@YouFound_Lxam
I'm sorry I haven't gotten back to you. I have a very busy week coming up. I should hopefully be able to get back to this on Saturday. If I don't post anything by then, just send me another reminder.
Created:
Posted in:
-->
@YouFound_Lxam
Why would you assume that a planet is not designed, but a light bulb is?What is the reasoning behind that assumption?
The most reasonable explanation for the existence of the planet is that it came together under gravity, since that is the way that planets usually form. Light-bulbs, however, do not tend to simply come into existence from natural phenomena; therefore, the most reasonable explanation for its existence would be intelligent life.
Time is not infinite, and since we have concluded that math is infinite, then it exists somewhat outside of time.Therefore, math is an infinite tool, that demands an infinite creator.
I agree with all of these things, including that if math were created, it would demand an infinite creator. I'm not sure what point you were trying to make by saying this. You seem to simply be reiterating what you said previously about the fact that math being infinite is not an issue if it has an infinite creator, which as I already explained, has nothing to do with the argument I made.
Created:
Posted in:
-->
@YouFound_Lxam
Then you admit that a complex design demands a complex designer.
You assumed that that was the reasoning that I used to reach the conclusions that I did. You assumed incorrectly. I do not admit that a complex "design" demands a complex designer. Instead of a rock and a system like Google, let's switch to a planet and a working light-bulb. I would reason that the planet was probably not created by an intelligent life form, but instead by matter naturally coming together under gravity after the birth of a star. I would also reason that the most reasonable explanation for the light-bulb would be that it was created by intelligent life. The information contained in the planet is immense, the complexity of the interactions between its atmosphere, geological phenomena, and other systems is mind-blowing. An uncountable of chemical reactions occur on its surface every second as tectonic plates shift, weather patterns and storm systems emerge, and complex processes create fascinating geological formations over time. The light-bulb on the other hand contains a few wires, so metal and glass, some electrons running through the wires, and some nitrogen gas inside the bulb. This example illustrates that simply using complexity as our standard for whether or not something had an intelligent creator is a gross oversimplification.
But math has not always existed.
How do you argue? I thought that we agreed that it exists outside of space and time.
If you are not infinitely complex, you can't.But if you have infinitely complexity, you can create anything, including infinite things.
My argument did not include "math is infinite therefore cannot be created," so this seems like a straw man.
It's only a logical contradiction, if you are assuming God is a finite being.
When did I assume that? I don't recall including that in my argument implicitly or explicitly.
Created:
Posted in:
-->
@YouFound_Lxam
Not the same logic at all.Rocks are physical pieces of matter that we can analyze and are not exactly complex.Math is a logic driven system of numbers and equations, that stays true throughout the entire universe.Rocks do not stay the same throughout the universe.
In my post, I said "The rock could even have many complex and interesting details." This was conveniently excluded when you quoted me. That rock can be as complex as you like. I'm still not going to be convinced that it was created by intelligent life.
Question:If you found rocks on a remote planet, would you assume there is intelligent life on that planet?Another question:If you found a complex system similar to Google on a remote planet, would you assume there is intelligent life on that planet?
For the first question, no, and for the second question, yes. This doesn't defeat my argument. My point was that it is not the complexity of something that determines whether or not it is reasonable to believe that it was created by intelligent life.
Your defense was just pointing out facts of math. It didn't defend any position about math not being created.
This was my argument:
To create is to bring into existence. This implies that the thing previously did not exist, and now does exist. If it did exist previously, it did not need to be created, and if it does not exist now, then it has not been created.
My point was that since math has always existed, it cannot have been created.
This is big.You admit the existence of a supernatural world, therefore you must logically admit to the existence of the possibility of supernatural beings.
I never argued that God could not exist because a supernatural world does not exist, so I'm not sure what this does for you.
Because everything that has a beginning, must have a cause.
Your use of "natural world" in the past few posts suggests that you consider it to be the same as the physical world. In this case, I will agree that everything in the natural world came into existence at some point.
Thats a logically incoherent statement and you know it.
I find it very strange that you would assert that I know that. How would you know what I know? Anyway, I will clarify what I meant by this. I originally asserted that you cannot create something if that thing exists regardless of your creation of it. It should hopefully be clear enough that creating something that already exists is a logical contradiction. You asserted that God can do this, presumably implying that God can do anything, even if it is a logical contradiction. My assertion was that even if it were true that God exists and is capable of such a thing, he never has done such a thing, and he never will do such a thing. I went on to explain why. I hope you can understand what I mean now.
Logic is the way our human brain perceives and thinks out things.God doesn't have a human brain.
My argument did not rely on what you just debunked.
Created:
Posted in:
-->
@YouFound_Lxam
The fact that we can do math, proves that math is an intelligent system.If we were to find a complex system like Google, on a remote planet somewhere, we would automatically assume that the system is a sign of intelligence. Even if we couldn't understand how the system works, doesn't take away from the obvious sign of intelligence.
By the same logic: Rocks are some thing that we can analyze, ("doing math" is just a shorthand for analyzing it) and therefore they are an intelligent system. Thus, if we see rocks on a remote planet, we should assume that there is intelligent life there which created those rocks.
Just because something can be analyzed in an intelligent manner doesn't make it analogous to something like Google. The rock could even have many complex and interesting details. That still wouldn't imply the existence of intelligent life.
Yes. What is your point with this.
I was defending my position that math cannot have been created.
So, you admit there is a natural world, and a supernatural world?
You aren't being particularly consistent with your definition of the natural world, but if it is the same as the physical world, then yes, I "admit" the existence of the supernatural world.
Does Morality exist?Does Math exist?Does Time exist?Does Gravity exist?
Yes, yes, yes, and yes. Now I'll repeat my question: Why is it that everything in the natural world must be created?
You can if your God.
Even if he can, he never has, and never will. Most people agree that God's omnipotence does not include being able to defy logic itself, but even if you do not agree with this, I would argue that God never has and never will done anything that defies logic. If he ever has or ever will, then truth could not exist in a meaningful way. This is because of a phenomenon known as vacuous truth. If so much as one logical contradiction exists, independent of space, time, etc., then every statement is both true and false. For the following, I will simply use "-" to represent the negation of a proposition (-P means "P is false"). Suppose some logical contradiction exists (once again, regardless of where or when or if it is even within the bounds of space and time). Then P and -P are both true for some proposition P. Suppose Q is any proposition. Then -Q -> P since true propositions are implied by all other propositions. Taking the contra-positive, -P -> Q. But -P is true, so Q is also true. We can apply the same logic to the proposition -Q. It follows that Q is both true and false for any proposition Q.
Well, if God didn't exist, then nothing would exist, because God would have to create everything, so there would be no Mandelbrot set, and no computers, and no humans to type that in, and no math, and nothing.
Which argument for God am I up against exactly?
Created:
Posted in:
-->
@YouFound_Lxam
But math in of itself is a sign of intelligence.
What do you mean? Doing math is a sign of intelligence, yes, but the Mandelbrot set was the Mandelbrot set before anyone plugged the numbers into a computer, and if you disagree with that, then you are effectively saying that said computer created it, which would defeat your entire original argument.
Again, if this intelligence goes beyond time space, and matter, then it can also create things beyond time space and matter. How do your account for the fact that math is infinite, but the universe is finite?
To create is to bring into existence. This implies that the thing previously did not exist, and now does exist. If it did exist previously, it did not need to be created, and if it does not exist now, then it has not been created. As to your question, it's simple: Math is not contained within the physical world.
Yes, the concept of a unicorn exists in the natural world.
Okay, so we extend the natural world beyond the physical world. Why is it that everything in the natural world must be created?
Yes, but I wouldn't phrase it like that. I would say that there was a point where time came into existence.
You deliberately ignored the part where I point out that your statement is self-contradictory. As I have already pointed out, "always" is a temporal word, so your statement does indeed imply that there was a time at which time didn't exist, that it, there was a point at which time did and didn't exist. Regardless, your new phrasing would suggest a different interpretation: Time had a beginning. This I would agree with. Nonetheless, math existing outside of time means more than that it has always existed. It means that it also exists in states of reality (not exactly "points in time" anymore) in which there is no concept of time whatsoever. The point is that you cannot create something if that thing exists regardless of your creation of it.
Now I have a question for you. You claim that the Mandelbrot set was created by God. In a theoretical in which God did not exist, when the formula for generating the Mandelbrot set was plugged into a computer, what would happen?
Created:
Posted in:
-->
@YouFound_Lxam
My apologies. Let me more clearly outline what i am referring to. I am saying that something that is a part of our natural world, that exists in our natural world, cannot have no cause. God, in order to be correctly defined as God, would have to not he bound by time, space, or matter. Therefore, he would have exist outside of our natural world, making him supernatural.
Math is not bound by time, space, or matter, therefore you should hopefully agree that it requires no creator.
True. But since we also utilize math, it also exists in our natural world, so it would logically have to demand a beginning, and creation, preferably by something beyond its capabilities.
So if I write an allegory, and someone applies it to their lifestyle, the allegory exists in the natural world? If it exists in the natural world, then so does everything that it contains. If the allegory contains a unicorn, and the allegory is applied to the natural world, then by your logic, unicorns exist in the natural world.
But, time has not always existed. You can have an infinite future, but you cannot have an infinite past, otherwise it would be impossible to make your way to the present.
"Time has not always existed" huh? So there was a point in time at which time didn't exist? Seems self-contradictory to me. And before you argue that my rephrasing of your original statement misrepresents it, keep in mind that "always" is a temporal word. Always is literally defined as "at all times." (https://www.merriam-webster.com/dictionary/always)
Created:
Posted in:
-->
@YouFound_Lxam
But something can't just be. Something can't exist without being created in some way shape or form.
Why? If you consider God to be the creator of all other things, than God was not created. I have often heard the argument that God exists outside of time, and so is separated from causality, but the exact same thing applies to math. Math is effectively the study of those truths which are absolutely necessary. This shape, and everything else in math, exist outside of time just like this proposed God. (Perhaps you do not assert the existence of such a God, but your bio states that you are Christian, so I assumed as much.) In fact, that which is outside of time has, at any point in time, has always existed, which is in contradiction with its creation. By this logic, math cannot have been created. Oh look! Since the Christian God is supposed to have created everything, I just accidentally disproved the existence of God as defined in Christianity!
Created:
Posted in:
Is "I think therefore I am." really accurate? The use of "therefore" suggests that this is a deductive argument:
P1: That which thinks is.
P2: I think.
C: I am.
But why? We presume that we think, but what does it even mean to "think?" If it is simply the processing of information within the brain, then computers think. Not that this invalidates the argument because computers don't exist, but rather, it just shows that this definition of "think" doesn't really hold up. More importantly though, why is the first premise true? For what I have to say next, I will first attempt to establish that everything is simply, at its core, information. A thing is defined solely by its properties, that is, by being what it is. In this sense, a thing is the information that it contains. However we chose to define "think," it seems reasonable that it would pertain only to what happens within the mind of the individual. But if you accept the premise that everything is, at its core, information, than one could conceivably create a thinking mind just by imagining it. But then that mind does not exist in reality, in contradiction with the first premise. But then, if we accept the premise that everything comes down to information then isn't our own universe only as real as that mind? In that case, perhaps "I think therefore I am." is correct, and can in fact be generalized to "I have meaning therefore I am." Every thought, every idea, every belief, every concept never considered, that which is not even imaginable, the world of magic imagined by a 7-year-old, all of it is real.
Created:
Posted in:
-->
@YouFound_Lxam
Basic common sense would say that someone designed this, but no human designed it.
...except that sometimes the universe defies our "common sense." Amazingly, this quite literally infinitely intricate shape is merely a logical inevitability. By this I mean, from the rules selected (z^2=z+c, the iteration process, checking if it remains bounded, etc.), this shape is the only one that could ever arise, independent of any sort of god, or of us, or of the physical universe, or of any sort of supernatural force external to the physical universe. If you were to truly perform the tedious task of breaking every step of this down to its purely logical roots, you would see it for the logical inevitability that it truly is. This is what makes math one of the most intriguing subjects. It doesn't need to be created by anyone or anything. It doesn't need to be caused, or to be brought into existence. It just is.
Created:
Personally I have accepted autism as a critical part of me inseparable from my personality, and frankly I would rather be in that category then the "massive ego" category.
Created:
I psychologist I know once commented that to be interested in debate, you either have to be on the spectrum, or you have to have a very big ego. She wasn't making a joke either.
Created:
This "math overhaul" is ridiculous. Sure, if students are struggling, we should make math more intuitive for them, but that doesn't me that we should dumb it down or even eliminate it. Firstly, the concept that gifted students can just be shoved in with struggling students and then learn the same "big ideas" at different levels will never work, and advanced students will only be held back. Speaking from personal experience, schools already love to find excuses to keep students who are gifted at math in the same classes as everyone else, and this would only make that issue worse. A student at calculus level and a student at algebra level will never be learning the same "big ideas," and trying to force this on them will only drag students down. If parents ask for their child to be place in a higher class, even if they have real evidence to back up the fact that their child is significantly advanced, they may simply be told that their child was already being taught at their level, even when they are being lumped in with average and even struggling students. Secondly, this new curriculum will barely even teach math. The idea of keeping math in touch with reality has been taken too far. Students who end up actually pursuing a career in math will not be prepared for the abstract and theoretical. Moreover, this idea that there are "multiple roads" to calculus is ridiculous. If you want to learn calculus, you will need to understand algebra and trigonometry, not data science, computer science, or financial algebra. The topics of data science, computer science, and financial algebra aren't even topics in math! Data science and financial algebra are applications of math to business and economics, but they are by no means themselves areas of math, and working with computers will at best build some intuition for mathematical thinking in the form of coding, but computer science is not in and of itself math. (To be absolutely clear, theoretical computer science, which is the math behind the mechanisms of computation, is certainly an area of math, but this is at the very least college level, and between this and their focus on the real world, it is certainly not what is being referred to here.) Lastly, the example of a class activity given is especially concerning. Going on about how "everyone has their own strengths" and we are part of a "mathematical community" could possibly be somewhat inspiring, but is better suited for a team-building exercise, and not math class. This activity is a waste of time that will not do anything to improve mathematical intuition. That "mathematical community" won't help you if they're too busy drawing colorful lines to do actual math.
Created:
Posted in:
-->
@John_C_87
Yes, you are correct and thank you, Newton's work in trigonometry just sticks in my mind better for some reason. I am under the weather and willneed to come back to some of this in a couple days.
Okay, I understand. I hope you feel better soon. I will still respond to what you wrote in this post, but I will be patient for a response.
It is a machine error or specifically a human judgment call directing the error the machine makes.
You are only reiterating the same argument that I have repeatedly explained the irrelevance of. You will need to point out an error made in my argument, rather than some other one. My argument did not involve the use of a calculator, so claiming that this is where the error lies is nonsensical.
As we are going to go back and forth with this and in the end, we need a few more different rulers if you agree with me I am going to rest.
This is true. I agree that it is not productive if we simply go back and forth with the same thing over and over. I honestly don't see how calculator or computer error is relevant here, but if you could explain that, I will try to have an open mind.
Created:
Posted in:
-->
@John_C_87
I am going to disagreeand say there are multiple infinite numbers of decimal numbers
There are not "multiple infinite numbers of decimal numbers." The cardinality of the decimal numbers is the continuum, which is one infinite number. I don't even need to address what you say after this because operations on a set have nothing to do with its cardinality.
Created:
Posted in:
-->
@zedvictor4
But strays from the simplicity of the fraction decimal incompatibility in this instance.
This is a counterargument how?
Created:
Posted in:
-->
@John_C_87
I cannot say Pi is useless it just happens to be closer to a ratio of 4: 1 than 3: 1 adn tht is the reason it almost works when using Trigonometry.
It does not "almost work" when using trigonometry, it works when using trigonometry. I'm really not sure what you were trying to get at here.
It is trigonometry Isaace Newton formulated as a mathematic and what he had done is added woprk to Achemidese efforts in calculus.
Isaac Newton and Gottfried Leibniz invented calculus, not Archimedes. We've been over this.
No it is the error in mathmematics at the binary level in calulator and calulating systems the chips and low level coding create the infinite decimal.
You insist on attacking a source that I am not even using. In my arguments that 0.99999... = 1 I have at no point made use of a calculator, so your insistence that it is a result of calculator error is ridiculous. This would be like if someone told you that the Earth was round, and you responded with "well, you can't trust wikipedia!"
Achimedes and the whole Roman empire for a period of time had used a 1/12 fraction as a decimal in place of 1/10 or much of the Romen Empires money.
What's your point?
Created:
Posted in:
-->
@zedvictor4
And so on.
"And so on" won't be enough to magically generalize your argument to the infinite case. 0.99999... with n nines is alway 10^-n away from 1, but this difference is 0 with infinitely many nines, as the limit as n -> ∞ of 10^-n is 0.
Created:
Posted in:
-->
@John_C_87
The metaphoric nature of this debate is about Stars, Solar System, Galaxy, and Universe. The debate used infinite numbers created by a calculator to do this, it is the calculator which creates the idea of endless space that a sum may fill. This is not the identical reasoning and logic behind the infinite universe. The bus video is taking this scaling condition in a different direction than the # 0.99999 issue of the debate and the infinite concept of an unexplained volume in a boundless universe.
This debate has nothing to do with stars, the Solar System, the galaxies, or the universe, nor does it have anything to do with calculators, despite your insistence that it all comes down to calculator error, which is false. As I have already explained, calculators are entirely unnecessary to prove 0.99999... = 1.
Created:
Posted in:
-->
@John_C_87
Odd enough yes the derinition Wiki uses for Pi describes the sum of by being unfit to use in any calculation that requires a sum.......
Yes, the decimal expansion for π is basically entirely useless within the field of pure mathematics. π itself, however, is most certainly not. π is very important in pure math and the real world. Also, regardless of usefulness, π decimals expansion most certainly is valid.
meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers
The fact that π is transcendental means nothing about its decimal expansion. It is a fact about the number itself.
I can even quote you as you have said the 3.14159 is not used instead a veriable vlue symbol is used π.
Yes, that is correct. There is no good reason to use the decimal expansion as opposed to the symbol, at least in the context of pure math.
Created:
Posted in:
-->
@John_C_87
Groups and sets have everything to do with fraction stranslated and written as decimals.
No, they don't. Groups and sets are abstract mathematical objects defined in contexts well beyond the real numbers. Even in the context of the real numbers, however, sets themselves don't have anything to do with the conversion of fractions to decimals.
As does calculus
No, it doesn't. Calculus is effectively the rigorous study of infinitesimals. Calculus doesn't have anything to do with converting fractions to decimals.
According to Archimedes and mathematics the infinite decimal does not exist.
Infinite decimals are a well-defined mathematical construct: https://www.dpmms.cam.ac.uk/~wtg10/decimals.html#:~:text=To%20begin%20with%2C%20one%20defines,7%2C8%2C9%7D
Citing Archimedes property is just the wrong as a call addressing infinite in relationship to irrational decimals as irrational numbers.
The Archimedean property is a provable mathematical fact, so under no circumstances is it wrong to cite it while proving another mathematical fact.
The guy wrote Calculus....
First of all, this is blatantly wrong: https://amsi.org.au/ESA_Senior_Years/SeniorTopic3/3b/3b_4history_1.html#:~:text=Today%20it%20is%20generally%20believed,turn%20of%20the%2018th%20century. Second of all, how is this relevant?
Everything in the video has a fixed value. No, it started that way but quickly changed...the hotel for all we know has an infinite number of buildings, one for each bus. The buildings only hold 10, 100, 1,000,10,000., 100,000, 1,000,000, 10,000,000, 100,000,000, and 1,000,000, 000 people as so we can identify by series the truth of infinite. The real issue is that the calculator is just having sex and multiplying like a rabbit the sequence of 0.99999 is a flaw in the calculator’s design. Rights Reserved Patent pending.As a mathematician a person has a certain obligation to uphold a standard of morality when issues of human safety are involved with instruction of mathematics. Laws of education govern only the principle of instruction not injustice or legal negligence, it is law of negligence and other laws which does this. Usually,. Not always by usually…
In the hypothetical it is just one building: The hotel. Where the buses come from is irrelevant, since as I explained earlier, everything in the video is a stand-in for an abstract mathematical object. Metaphors don't have to be realistic so long as they represent what they are meant to represent effectively. You bring up calculator error again. As I have already explained, calculators are not relevant here. As to all the stuff about morality and legal negligence, this has not the slightest hint of relevance to this discussion.
Created:
Posted in:
-->
@John_C_87
The video is not meant to be a counter argument. lol......
That's not what I said. I was referring to this:
Infinite people, infinite buses, infinite rooms, andinfinite hotels...Are to be proven that is the Hypothesis. The groups ofpeople on the bus do not end, nor do the groups of rooms in the hotels. The veyuse of odd even rooms in the video, the people on the buses are all still allpeople, simply the infinite group is on every bus to be counted in simultaneoussequence.
how does anyone counter a theoretical condition we are pretending which is describing a scenario with its own goal not condition set to be factual sound prinicples. Please do not get me wrong I like the video it is simply not how I would describe it, that is all. Again I am sorry I can get offensive. As fact we agree there is no such thing as an infinite number of people, correct? Conflicts change when theoretical conditions are not meant to be argued as a truth. Again, the video is a lie made to prove a point. Point taken. I am just giving a limited point of view on logic and reason. Honestly it was a great video all things aside.
We agree that there is no such thing as an infinite number of people, but the "people" in this video are a more intuitive way to represent abstract mathematical objects like the natural numbers that do indeed exist in infinite quantities. The video is effectively a fictional metaphor for a very real mathematical phenomenon.
I have gone over with "zedvictor4" thereis no infinite number of nines it is a low-level program error in a calculator.Nothing more than the numbers repeating is nothing but a choice over cost effective production of calculators and the computer age ate it up like prime beef or a meatless steak if we role that way. We have cited the work Archimedes and the issue had been made clear Centuries ago by his work.
You keep referring to calculator error. At no point have I made use of a calculator in my arguments. I am discussing the fact that 0.99999... = 1, which is provable without use of a computer, calculator, electron microscope, or any equipment whatsoever. One simply needs the definitions, and 0.99999... = 1 pops out as the result of a step by step logical argument. I discussed this in post #14, but I can lay out the argument in more precise, rigorous detail if you would like.
Created:
Posted in:
-->
@zedvictor4
Yep.There is a reason for an infinite number of nines.And I just explained why.
This is the first time you have spoken on the case with an infinite number of nines, so no, you didn't "just explain why."
Created:
Posted in:
-->
@John_C_87
Infinite people, infinite buses, infinite rooms, andinfinite hotels...Are to be proven that is the Hypothesis. The groups ofpeople on the bus do not end, nor do the groups of rooms in the hotels. The veyuse of odd even rooms in the video, the people on the buses are all still allpeople, simply the infinite group is on every bus to be counted in simultaneoussequence.
If this is meant to be a counterargument, I don't see what it proves.
Yes.......no, mathematics states Pi is invalid.
Mathematics does not state that "π is invalid." That's ridiculous. Could you link to a source which states this, or prove that "π is invalid?"
Created:
Posted in:
-->
@John_C_87
If a infinite number of people on / in one objectis to true. All other buses are empty as fact. There are an infinite number of buses but only one bus of infinite people, as there are no people left to go on any more buses but one. "The whole idea on the video is a lie. Not even a good lie at that." Understand?
There is no reason that there necessarily wouldn't be any people left to ride the other buses. Since this is a hypothetical, we can have as many people involved as we want. If there aren't infinitely many people on every bus, we just add more into our hypothetical. If you would like to demonstrate why it is a mathematical impossibility not to have more than one infinite bus full of people, please present a rigorous proof, rather than simply declaring it as fact.
It is part of a minor math discrepancy about the video. When describing the bus and people in calculus the letters a and b would be written as buses y and z they are variables not fixed values.
Everything in the video has a fixed value. The cardinality of the hotel and of the buses is aleph null, and the cardinality of the party bus at the end of the video is the continuum. (see the second meaning of "continuum" on the linked webpage) Cardinal numbers never show up in calculus, but this isn't calculus, it's set theory.
Created:
Posted in:
-->
@John_C_87
"I had written.""I respectfully disagree on what is stated as the Archimedean Property uses the symbol ∈ describing a membership between real numbers the letter ( a ) can describing in calculus a value which is fixed and the { } brackets identify a set."
Exactly. { } brackets identify a set, not a group. As I explained, in math, those are two different things. It's an important distinction.
1. We have a membership to group by the use of mathematic"∈" symbol means membership and well it is ArchimedeanProperties we are speak of here.
Yes. Except that the Archimedean property has nothing to do with groups, but rather this symbol is used in the more general context of sets.
Groups and sets are two different things in the context of math. It's really not that hard of a concept.
2. The bracket { } identifythe math principle of set in all math notation not just Archimedean property.
Correct.
3. Archimedes’ work is on calculus which is in general explanationbrings mathematics of calculus in to describe x as a "little bitof" or most often described as " an element of."
Correct.
The whole ofcalculus describes the topic of element as of being more than on so is sets andgroups of elements.
Calculus and group theory really don't have much to do with each other. Especially not the Archimedean property.
Calculus has a lot to do with sets but sets and groups are not the same.
I'm not going to focus on "Pi" as it was part of a list of mistakes to corect. I have always felt this error in desperate needing of a solution. The topic at this point may drive us toa lesser understanding at the moment. On a personal note, I have resolved anyissues with a approximation of Pi, writing a new formulation in trigonometry as theterm cPi using work from Isaac Newton's trigonometry, whereas triangles bothright and left 90 degree angles can be used to calculate circumference as hypotenuseof those respected 90 degree angles. as the letter (c) suggest in calculus Ihave a created a formula that sets a constant that is not irrational as value.
I'm not sure I follow. Are you claiming that the decimal expansion of π is invalid? You reference a formula that you yourself apparently created. Would you care to share this formula in exact mathematical detail?
In the above exsample did all of the mathematic symbols translate across to this forum.They didn't for me and the math symbols of a triangle with the apex facing right or left is the principle missing for subgroup here.
As far as I know, all symbols are appearing as they should.
Created:
Posted in:
-->
@John_C_87
There is no such thing as a group of people as sets of infinite people infinite describe all the people as one normal group.
This sentence isn't the most readable, but if I'm interpreting it correctly, you are saying that an infinite group of people. That is true. The video is just using something concrete (people) to assist in the explanation. It is not being suggested that any of this could actually happen. Only in the abstract. As the video says, this line of inquiry lead to the invention of the modern cell phone and computer, so if it's all wrong, then I'm not sure how it's possible for us to have this discussion.
The bus as explained in the video is stating that a lie is taking place somewhere.
This is simply false. The video does not make reference to any sort of "lie."
If bus (a), being a set value in calculus is in fact infinite there is no bus (b) as set value. Bus (a) is holding all people. otherwise, bus (a) is properly called bus (x) and is an approximation value only.
Could you please explain what is meant by bus (a), bus (b) and bus (x)?
Created:
Posted in:
-->
@Best.Korea
Since infinite steps are needed, infinite time is needed as well.
Thank you for quite nicely spelling out the fallacy in your reasoning: You seem to think that an infinite number of steps cannot be done in an infinite amount of time, as this very example proves.
If logic proves something that is counterintuitive to you, that is probably because you simply find it counterintuitive, and not because the logic is wrong. You haven't actually pointed out a flawed step in my reasoning. Rather, you just declare that the conclusion makes no sense.
Created:
Posted in:
-->
@John_C_87
The error here is the choice in numerical decimal systemthat creates the 0.9999... in the first place. This is not the only error in mathematics,or the only location is a string of formula where error occurs. In post #14 we established only that 0.9, 0.99, 0.999, 0.9999, etc. are groups of subsets of #1 not that they had been precise. We are also describing the use of duodecimal system to negate fractions decimals like (0.9, 0.6, and 0.3).
This is indeed a flaw in the decimal system, and it is indeed a human error. This is why mathematicians generally avoid using it. For example, if you ask a mathematician "What is the area of a circle with radius 1?" they will probably not say "3.141592...." Instead, they will probably say "π." You mention the duodecimal system. While it is better, the same issues still remain: 0.BBBBB... = 1 in duodecimal. If you would like to propose a way to avoid this issue, please do. I would love to discuss it.
I respectfully disagree on what is stated as the Archimedean Property uses the symbol ∈ describing a membership betweenreal numbers the letter ( a ) can describing in calculus a value which is fixed and the { } brackets identify a set.
We must be misunderstanding each other here. I agree with this.
meaning group,
Now I understand the issue. "Group" and "set" do not mean the same thing in math: group, set. Please familiarize yourself with these definitions.
Some subgroups are Irrational numbers or Natural numbers they are not all "normal." We can compare Time, Degree, Prime, Natural, Irrational, Rational, Odd, Even, etc. and see this.
I would blame your misunderstanding of the term "group," except that all subsets (subgroup or not) of the real numbers satisfy the defining property of a normal subgroup, so I'm not sure where you are getting this from.
This is the definition provided by you of normal subgroup:
In abstract algebra, a normal subgroup (also known as a invaariant suibgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words,a subgroup N of the group G is normal in Gif and only if gng ^ -1 element (∈) N for all g element (∈ )G and n element ( ∈ )theusual notation for this relation is N normal subgroup (⪦ )G
If S is any subset (not just a subgroup) of the real numbers, then gng^-1 = gg^-1n = n ∈ S by definition of g^-1 and by the commutative property for any n ∈ S and g ∈ G, G here being either the multiplicative group of real numbers, or the additive group of real numbers, whichever you were referring to.
Created:
Posted in:
-->
@zedvictor4
You directed me to post #27:
0.9 = nine tenths.Therefore ten tenths = 1.0.99 = 99 hundredthsTherefore a hundred hundredths = 10.999 = 999 thousandths.Therefore a thousand thousandths = 1And so on.
Here you demonstrate that 0.99999... is not equal to one in the case of finitely many nines. I just clarified that I am referring to 0.99999... with infinitely many nines, yet you fail to address this. I will wait for you to address the case of infinitely many nines.
Created:
Posted in:
-->
@b9_ntt
The fact that the set of all integers contains more terms than the set of all even or odd integers renders the word more (or greater than) meaningless.
These sets are all, rather counterintuitively, the same size. There are, however, sets that are bigger. This video explains it better than I ever could.
Created:
Posted in:
-->
@zedvictor4
And I easily demonstrated that 0.9... will always fall .1 or .01 etcetera, short of 1.No rigour required.
You demonstrated that 0.99999... falls short of 1 for finitely many nines. I believe I have already clarified that I am referring to 0.99999... with infinitely many nines. Please explain how you would demonstrate that that falls short of 1.
Created:
Posted in:
-->
@John_C_87
"Everyone needs to have an Electron Microscope to observe as a witness the error as it is made in mathematics and how it occurs ,or it is otherwise seen as human failure only."
There is no error involved, so I don't see this as relevant. You may claim that 0.99999.. = 1 is dependent on error, but that is simply false. I demonstrated in post #14 that this follows from the definition of an infinite decimal.
The idea is not to disprove Archimedean Property, the objectis to establish it is not mathematically relevant. Archimedean Property are classifications of subsets and mathematic elements. The Archimedean Property describes that ( 9.0 ≠ 10 ) as ( 0.9 ≠ 1.0) stating that as fact9.0 and 0.9 are normal subgroup( ⪧) the idea is not to disprove Archimedean Property the object is to establish it is not mathematically used relevant. Archimedean Property are clasifications of subsets and mathematic elements. The Archimedean Property describes that 9 is boundary.
The Archimedean property states that if x is a real number there exists some natural number n such that n > x, so the Archimedean property has nothing to do with subsets or normal subgroups, nor does it "describe that 9 is a boundary." Also, yes, 0.9 is not equal to 1, nor is 9 equal to 10, but 9 and 0.9 aren't "normal subgroups" of anything. A normal subgroup is a type of subgroup, which is in turn a subset of a group that is also a group. 0.9 and 9 aren't groups.
In abstract algebra, a normal subgroup (also known as a invaariant suibgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words,a subgroup N of the group G is normal in Gif and only if gng ^ -1 element (∈) N for all g element (∈ )G and n element ( ∈ )theusual notation for this relation is N normal subgroup (⪦ )G
All subgroups of the real numbers are normal, so I don't see this as relevant. This is in fact true of any Abelian group. (A group that satisfies the communatative property.)
Created:
Posted in:
-->
@Intelligence_06
yees
I would have to agree, considering that there aren't any generally accepted strong definitions of existence that I know of.
Created:
Posted in:
-->
@John_C_87
Archimedean Property does not consider laws of thermodynamics. Archimedean property applies a rule of scale and proportion which is not by fact accurate by laws of thermodynamics or in line with human margins of error. 0.9 is proportional to 0.999999 they are equal though are not secureas equal by precise measurements and are subject to change, such low values are demonstrated to change by the choice of letters assigned in Calculus near theend of the English Alphabet.
I'm not sure what the sure what any of this has to do with the Archimedean Property. The proof of the Archimedean property is purely done in the abstract mathematical setting with no relation to thermodynamics or physics more generally. For that matter, nothing you present here addresses the proof of the Archimedean property. Also, no, numerical constants don't change. You seem to be referring to measurement error in computers, which is not relevant in the context of pure mathematics, where everything is done rigorously and precisely.
Not everyone has or can work an Electron Microscope to establish that there is no natural value of 0.999999 and those values created by computers and calculators are fabricated and not calculated by poor practice in calculation. There are several examples of this throughout the history of mathematics as science has evolved over the years. The formula to write 0.9999 is more complex thus taking more work than that what is for most people is not needed to do to acquire the sum which will suit a given purpose during normal math routines...
Not only does not everyone have an electron microscope, no one needs one to verify that the proof that you quoted (which is the standard proof of the Archimedean property) is valid. Also, errors in computers and calculators are irrelevant. No computer or calculator is required in this proof.
You have not disproved the Archimedean property. You have mostly just talked about errors in computers, which is irrelevant to this discussion. If you are confident that the Archimedean property is wrong, provide a counterexample:
The Archimedean property states that if x is a real number then n > x for some natural number n. If this is false you should be able to provide a real number x for which I cannot provide a natural number n that is greater than your x.
All you need to respond with is one number. It just takes one number to prove me wrong. Given how well-substantiated this simple mathematical fact is, I am highly doubtful that you will be able to provide such a number.
Created:
Posted in:
-->
@Intelligence_06
It is not that I am not interested. My view on this topic is that what truly exists is determined by you. Something exists to you just because you can sense it or can prove its existence(namely places that you have never gone before, etc). It does not matter any discussion on existence outside one's senses unless we are talking about ideas. Oh wait, ideas are still dependent on the minds of one.
So you are of the position that existence is subjective?
Created:
Posted in:
-->
@zedvictor4
One can only work on assumptions relative to the self-contained.Though if our assumptions are reasonable, I would suggest that existence is relative to the speed of time.And the speed of time is seemingly........Infinitely fast......Making existence immeasurable.Past and future are perhaps only self-contained mental exercises.
One could then ask what makes the present the present? We can't just say the present is what's happening right now, because "now" relies on the present. And if the present doesn't exist, and nor do the future or the past, what does?
Created:
Posted in:
-->
@zedvictor4
I forgot to add you as a mention in the above post, but it was directed at you.
Created:
Posted in:
0.9999....Never equals 1.
You have only demonstrated this for finitely many nines. "0.99999..." is intended to denote infinitely many nines after the zero. I demonstrated rigorously 0.99999... = 1 in posts #14 and #22 and demonstrated it nonrigorously in post #1. I await a counterargument which applies to the case of infinitely many nines.
Created:
Posted in:
-->
@Intelligence_06
Why does it matter?
Honestly, I don't have a good answer to this question. If you aren't interested, then you don't need to participate in this discussion.
Created:
Posted in:
-->
@RationalMadman
Supply us the definition of 'exist' you wish us to employ in this thread.
In the past, I have attempted to bring up the issue of a lack of meaningful definitions of "exist." The response to this was that the question was stupid and everyone knows what "exist" means. All arguments to the contrary were deemed irrelevant. So I'll be honest with you, this is a more subtle way to bring up the same topic, so you tell me, without using similar words such as "real," (unless you intend to define them separately) how would you define "exist?" Then we can work with that definition.
Created:
Posted in:
A few questions to ponder and discuss:
- Does the past exist?
- Does the future exist?
- Do abstractions exist?
- Do thoughts exist?
- If something will never be observed, does it exist?
- If you have heard that something has been observed, but never observe it yourself, does it exist?
Created:
Posted in:
-->
@zedvictor4
Are you sure that's enough?And is that the point at which matter ceases to exist?
He was making a joke.
0.9 = nine tenths.Therefore ten tenths = 1.0.99 = 99 hundredthsTherefore a hundred hundredths = 10.999 = 999 thousandths.Therefore a thousand thousandths = 1And so on.
What's your point?
Created:
Posted in:
-->
@zedvictor4
Certainly to a large extent, but there is still some significant randomization.
Created:
Posted in:
-->
@zedvictor4
Does 0.9 = 1?No because the difference is significant.Does 0.99 = 1?No because the difference is still significant.So how many 9's are required to make the difference insignificant?
You seem to be holding the following common misconception: That 0.99999... = 1 because the difference is so small that it is insignificant. 0.99999... is exactly equal to 1. They are the same number. No rounding is happening, nor is anything being approximated. We generally would intuit a decimal like 0.99999... to be a number ever so slightly less than one, but such a difference would have to be infinitesimal, and infinitesimals do not exist in the real numbers thanks to the Archimedean property.* I suppose in a sense, 0.99999... = 1 because the difference is so small that it can't even exist!
This proof isn't exactly my favorite, since it doesn't provide any intuition on what 0.99999... and other such decimals are defined to be, but it does demonstrate something else valuable that other proofs cannot: Any reasonable definition of 0.99999... (where 0.99999... is at least 0.999...9 for any finite string of nines, and is no more than 1) must have 0.99999... = 1. This is important because it shows that this is not a quirk in the way we define infinite decimals like 0.99999..., but a quirk in the real numbers themselves.
*If you aren't sure why this implies that infinitesimals can't exist, if a positive infinitesimal is defined as a number greater than zero but less than 1/n for every natural number n, (which 1 - 0.99999... would be if it were positive) than if x is a positive infinitesimal, x < 1/n for every natural number n, and so 1/x > n for every natural number n, a violation of the Archimedean property.
A bonus more technical note if you're interested:
In other number systems like the surreal numbers, there are infinitesimals. It is not true, however, that 1 - 0.99999... is an infinitesimal in this context. Rather, all decimals retain their original values when extending like this, we just also add new numbers which cannot be represented as decimals. How we denote numbers is of course a matter of convention, but as the algebraic argument (see my original post) demonstrates, if we want decimals to satisfy certain nice algebraic properties, we must have 0.99999... = 1. For that matter, number systems like the surreals aren't used as often because by getting rid of the Archimedean property, we also have to give up completeness, which is really important for calculus to work the way it does.
Created:
Posted in:
-->
@Best.Korea
There is a weak sort of free will in that, as modern theoretical physics asserts, everything in the universe is non-deterministic. This is, however, merely random noise. Basically, you have as much free will as a computer program with the occasional input from random.org.
Created: