I don’t feel convinced, I feel like you’ve begged the question there a bit. Your explanation for why you can’t split 100% of ten eggs into 3 equal parts ended up relying on the assumption that you can’t split 100% of anything up into 3 equal parts. In other words, it seems to me as though you’re assuming your conclusion in order to prove your conclusion, which seems circular to me. I of course may be missing something.
May I ask you some questions now?
Ask away.
But in order for you to claim that 10 eggs can be split into 3 equal parts you need to tell me what % each part is, and they must add up to 100%.
If you did this with splitting 10 eggs into 8 parts, the first split would be 1 egg (100%) for each part (8 eggs) and 2 remaining eggs. Now you need to divide the 2 remaining eggs into 8 parts. That is 200% divided by 8, or 25% for each of the 8 parts.
So 1.25 eggs (125%) for each of the 8 parts, and 8 x 125 = 1,000%, which is 10.00 (1,000 hundredths)
Okay, so I want to get a handle on the world where we’re dividing this egg first of all.
Is this an egg in our reality, or in some mathematically perfect platonic reality where we don’t have to worry about practical considerations, like how you can’t cut an egg with a knife without getting yolk on the knife?
I assume most likely we’re not concerned with the impracticality of getting egg on the knife, so I assume it’s some platonically perfect reality with perfect eggs. So my next question is this:
In this perfect platonic reality where we’re splitting this egg, is this reality in any way for any reason beholden to the base 10 numbering system, or does this egg that we’re splitting have no bias whatsoever to any particular base number?
We are obviously speaking about theoretical mathematical operations. Sure, there are also practical arguments, but we are speaking about math, not the practical limitations of splitting an egg into a million parts. Mathematically we can split the egg into a million parts, realistically we can’t.
I am discussing the theoretical mathematical operations of dividing a whole egg into equal parts. That obviously can’t be done in the real world. I am discussing the MATH of dividing 1.0 into equal parts.
We are using base 10 for now. Obviously an egg on the table doesn’t change just because you have a different base to describe it. An egg is an egg and couldn’t care less which base you use to describe dividing it.
No, the egg doesn’t have a bias to any particular base.
Once you understand that an egg can’t be equally divided into 3 equal parts in base 10 then we can find out if it can be done in other bases. That is a DIFFERENT question as to if it can be done in say base 6. We can have that conversation once we’re done answering whether it can be done in base 10 or not.
You can’t even admit that it can’t be done in base 10, so until you acknowledge the facts of base 10 there is no point moving on to other bases.
I will decide which points I make and which bases I use, just like you decide which points you make and which bases you use. I have ownership over my half of this conversation, I’m not telling you what bases you’re allowed to use or what points you’re allowed to make. Please allow me the same courtesy of choosing my own words, my own points, and even my own bases.
So, this egg isn’t biased towards base 10 and the universe it’s in isn’t biased towards base 10, we’ve established that now. Very good.
So, let’s say I agree with your line of reasoning. Let’s just imagine, for a second, that I agreed with you and your reasoning so far, which is as far as I can tell, “If I try to divide by some number X, and it produces an infinite decimal in base 10, that means we can’t actually divide evenly by X.”
BUT since we’ve established that neither the universe nor the egg have any sort of proclivity, preference or bias for base 10, then we should be able to change the above sentence to ANY integer base.
“If I try to divide by some number X, and it produces an infinite decimal in base Y, that means we can’t actually divide evenly by X.” Where Y is any integer I choose.
Would you agree with that? If not, why not.
I would agree that if a division can’t be equally divided then it will continue infinitely, and that means that you can’t divide that many parts equally.
If it were to divide equally then the division would end at some point and not continue infinitely.
So is the case for 1 divided by 3, the division can’t end, so you can’t have 3 equal parts. There is always 4 parts, 3 that are equal to each other, and 1 that is the remainder. 4 parts. It never equally divided into 3 equal parts.
I cannot tell if you’re agreeing to the question I asked or not. Do you believe that I can apply the “infinite decimal” logic to other bases, or does it only apply in base 10? Not trying to be pedantic, I just need it to be completely explicit.
Let me put it this way. You can speak about whatever you so desire, but I will not respond to your off topic responses using bases other than base 10. You know we are talking about base 10 for right now. If you choose to talk about base 6, for example, then I will ignore your off topic responses.
That way you do what you want and I do what I want. Fair enough?
I believe that if a division continues infinitely then the division is never completed, therefor the parts are not equal. If it continues infinitely then there is a remainder that continues on infinitely. That applies to all bases.
That way you do what you want and I do what I want. Fair enough?
No it’s not fair. A conversation where we ignore each other isn’t the purpose of this thread. If you wanted to ignore me, I could have saved us some time and just not engaged with you at all.
The first half of this conversation was entirely led by you. You asked questions, and I answered them. I didn’t try to find excuses to ignore you, because I am trying to have this conversation in good faith. If you’re done with the conversation now that it’s my turn, let me know, I can just lock the thread.
That wouldn’t be a very fair approach to the conversation though, and I’d prefer it if you didn’t take that approach. I engaged with your questions, then asked if I could ask some. These are my questions, so now it’s time for you to prove that you do in fact want an honest conversation.
Can I apply your logic about infinite decimals to other bases?
Edit: now that you’ve apparently agreed that I can apply that logic to any base, I’ll have to wait until I get home to show you the consequences of that
We haven’t come to any conclusion in base 10 and you want to change the subject. Why can’t you just admit that in base 10 1 can not be divided into 3 equal parts? If you admit that then we can move to other bases of your choice.
I view your desire to change bases as a diversion from the task at hand. Why can’t you finish this conversation about base 10 before you move on to another base? Don’t care to admit I am right?
Do you think 1 can be divided into 3 equal parts in base 10? You claimed it could be, and left it at that. Where is your proof that it can be? You dodged the questions of how many percent each part is by giving another fraction.
A percentage as a fraction would look like 25/100, but you blew that off too.
You want to give a percentage expressed as a fraction of each part? Then post it as for example 25/100 . Percent is how many Hundredths. How many Hundredths is each “equal part?”
Why can’t you finish this conversation about base 10 before you move on to another base? Don’t care to admit I am right?
I explicitly asked you if your claims were ABOUT base 10 or merely using base 10. You said “using”. I’ve interpreted that to mean that your claim about 1/3 is not ABOUT base 10, but merely using base 10.
If your claims are ABOUT base 10, then you’re absolutely right when you say that other bases are a distraction. if your claims are merely using base 10, then I have points to make using other bases
So, your reasoning seems to go (and please correct me if I’m wrong): in base 10, if you try to divide 1 by 3, you will get an infinite decimal due to a repeating remainder. Therefore, you cannot divide 1 by 3.
If any part of that is phrased incorrectly, please let me know.
We’ve established that there’s no bias toward base 10, so let’s apply this logic to another division in another base.
In base 6, if you try to divide 1 by 5, you will get an infinite radix-point-number due to a repeating remainder. Therefore, you cannot divide 1 by 5.
I believe that the exact same reasoning you used to determine that 1/3 is impossible can be used to prove that 1/5 is impossible, and also 1/4, and also even 1/2. For every fraction of the form 1/X, there is a base where you will get an infinite decimal with a remainder that you can’t get rid of.
I invite you to continue the conversation in good faith and cordial tone to point out the error in my logic. I don’t believe I’m being beligerent or insulting towards you, I’m merely making my own points as I gave you the chance to do as well. Please try to maintain the conversation in a healthy manner.
Maybe I should also make it explicit that 1/5, in base 6, is 0.111111… repeating.
I don’t understand the distinction you are making in the difference between “using” and “about.”
I am discussing 1 divided by 3 in base 10. Obviously we are talking about base 10, and I am using base 10 in my symbols.
When I write “9” in base ten I am talking ABOUT this many “0 0 0 0 0 0 0 0 0” USING base ten “9”.
Obviously there is no “9” in base 6 or 3 etc.
The symbols we are using in base 10 are 0,1,2,3,4,5,6,7,8,9.
3 x 10 in base 10 equals this many “0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0”
We write that in base 10 as a 3 in the Tens position, and a 0 in the ones position, so 30.0.
Other bases do not write “30” to mean that many, so it is an apples to watermelon comparison.
That’s a great question, and one that has actually been central to our conversation, even all the way back to the first page of your original thread. The distinction between “using” and “about” entirely changes the content of your claim, and whether it’s disagreeable or not, and how disagreeable it is. There’s a reason I’ve asked this question so many times since the beginning, so let’s go into detail on the difference.
7 is a prime number. This is a claim using arabic numerals. This is a claim using the base 10 number system. However, when I say it, I’m not making a claim ABOUT base 10, and I’m not making a claim ABOUT arabic numerals. I’m making a claim about the concept that the symbol “7” refers to. The symbol “7” refers to the a particular quantity, “o o o o o o o” ← that number of o’s is the concept that the symbol refers to. In base 10 arabic numerals, we symbolize that concept with a “7”, but in base 6 we would symbolize that concept with “11”. But my claim isn’t about the symbol, and my claim isn’t about base10, it’s about the underlying concept. Which means that I believe my claim applies to that concept, even in contexts where the symbol doesn’t apply.
So 7 in base 10 is prime, but 11 in base 6, which refers to the same quantity, is also prime. And it’s prime for the same reason - because it refers to the same concept, and the primacy of that concept is what I’m claiming. Any symbol that refers to that concept has the property that I’m claiming.
On the other hand, “7 is pronounced seven” is no longer a claim about the concept of the quantity. That’s a claim about language and about the symbols that we use to discuss numbers and values. I can’t take the concept that 7 refers to and apply the same statement across the board, “11 in base 6 is pronounced 7”. The scope of this claim is entirely different from the scope of the primacy claim. It’s disconnected from the concept, and entirely connected to other things.
“1/3 is impossible”. This is apparently your claim. There’s a few different things that this claim could be ABOUT.
It could be about the base 10 number system – you could be saying “you can’t divide 1 by 3 while you’re using base 10”.
It could be about reality, in some tangible or more abstract sense. You could be saying “real things can’t be divided into 3 pieces.”
We’ve previously established, I think, that reality, or even the platonic perfect “reality” that we use for thought experiments, doesn’t have any bias towards or preference for base 10. That means that those two claims are not equivalent. They’re not interchangable. They may both be true, but if they were both true, they’d be true for entirely different and unrelated reasons, because they’re different claims from each other.
“You can’t divide an egg into 3 pieces” vs “You can’t divide an egg into 3 pieces in base 10”. These don’t mean the same thing as each other. An egg exists in reality. Reality has no bias towards any particular base. In fact, I would say that the second phrase doesn’t have meaning at all. You don’t have eggs in base 10. Base 10 has no frame of reference for the thing we’re referring to as an “egg”.
So, are you making a claim about eggs? And thus, is your claim about eggs entirely independent of what base you’re doing the math in?
Or are you making a claim about base 10, and not eggs, and therefore you CAN divide by 3 in base 6, for example?
You’ve deliberately made the conversation about physical objects throughout all your conversations, which makes me think that you’re not making a claim about Base 10, but a claim about reality, or a claim about eggs. But sometimes, you seem to switch your stance and take a more modest approach, that your claims really are claims about base 10, and not about eggs or about reality. Getting a grasp of exactly what your claim is is vital for any conversation about it. That’s why I’ve always focused on that, from the beginning.
So, what’s the nature of your claim? What is it about?
I NEVER claimed “1/3 is impossible.” To the contrary I gave you an example of 1/3 of 12 eggs being exactly 4 eggs, and the 3 parts of 4 eggs totaling 12 eggs. 1/3 is 4 eggs, 2/3 is 8 eggs, 3/3 is 12 eggs.
I am not claiming 1/3 is impossible, my claim is 1 is not equally divisible by 3.
“1” and “3” are the base 10 “1” and “3”, not any other base, which is why I want to strictly speak about base 10, but you want to diverge into other bases as if to muddy the water.
In reality there is no such animal as dividing 1 object into 3 equal parts. That is a PRACTICAL matter of dividing down to the atom, which I assume you know is impossible. But practical matters aside, I am speaking strictly about MATH.
Obviously, putting practical matters aside and speaking strictly about math, you have to be doing the math in some base. Whether the different bases have different possibilities is an entirely different matter, which again is why I want to stick to base 10 at first, so as to find the answer to the question in base 10. Different bases might have different answers, so each base needs to be explored separately, which again you choose not to acknowledge by jumping all over the place using different bases. I want to talk about each base separately, but you are unwilling to do that. It’s like discussing what 2 + 2 equals, and you keep changing the subject to what 3 + 9 equals. See? Why can’t you just find the answer to 2 + 2 and then move on to find the answer to 3 + 9 after 2 + 2 is settled?
Okay, I see now, your claim is actually ABOUT base 10. That’s a very interesting change of pace. You’re still apparently blaming me for the direction of the conversation, but I want to show you the reason why it was pushed in this direction.
I didn’t WANT to muddy the water, I WANTED to clarify the water. So I asked you, explicitly, on many many occassions, what your claim is ABOUT. Your answer to that has been inconsistent and changing. I’m going to go through a few places where your words led this conversation into me thinking you weren’t talking ABOUT base 10. Starting with this:
So, I’m clearly at this point in the conversation putting a lot of effort into clarifying if your claim is ABOUT base 10 or USING base 10, and you clarify. You clarify with all capital leters, you are USING base 10. Given that you were choosing between two options, ABOUT and USING, and you chose USING, this to me is a very unambiguous signal that your claims are in fact NOT ABOUT base 10.
If we go back to the original thread, when I also tried to clarify the scope of your claim, you also said this:
So once again, when asked what your claim is about, you chose not to say “it is about base 10” but instead “it is about reality”.
And then your choice of examples. You choose physical objects. You choose eggs. Physical objects in real life don’t care about what base you’re using. The fact that your focus is on physical objects is another piece of evidence that your claims are not just ABOUT base 10, but are about reality. You’ve done yourself and your own ideas a disservice by focusing so heavily on physical objects, if your true claim is merely ABOUT dividing 1 by 3 in base 10.
If you wanted to communicate your actual idea more clearly, and not mislead anyone about the scope of your claim, (a) you could have clarified to me immediately when I asked if your claim is about base 10 that it is, in fact, about base 10 - your failure to do that is the BIGGEST contributor to the fact that I keep on bringin up other bases. (b) you should have literally never started talking about eggs or pies. Eggs and pies are physical objects, and since we’ve established that physical objects in physical reality don’t care what base you happen to be doing your math in, physical objects are a complete misdirection.
Your claim isn’t about eggs. Your claim is simply put as “You can’t divide 1 by 3 in base 10”.
The only reason I ever brough up any other bases is because of the choices you made in the conversations. You’re blaming me for it, but you were given so many opportunities to clarify the scope of your claim, and YOU chose to give inaccurate and misleading answers that muddied the water and misled me and any other reasonable person about the scope of the conversaiton.
This thread was started on the presumption of good faith. In good faith, I asked you to clarify the scope, I asked you if you were talking about base 10 or not. Your answer was apparently to the contrary. Was your answer in good faith? Were you just confused, or were you lying? Because misleading your conversation partner about your own beliefs and positions is the exact opposite of being open and sincere, and anybody can clearly see that that’s exactly what you did here. You misled me, maybe on accident - although I don’t know how it possibly could be an accident, it seems like a very deliberate choice, a choice you’ve repeated throughout numerous threads.
It was a mistake to open this thread with you. You are either deliberately acting in bad faith, or you don’t yet have the philosophical vocabulary required to act in good faith. If you can’t even clarify the scope of your claims when asked, that’s either deliberate or a debilitating philosophical disability. If it’s the former case, you’re a troll. If it’s the latter, then I hope you’re able to figure it out one day. Clarifying the scope of your claims is a philosophical skill that anybody who wants to engage in good faith needs to learn to do. You need to learn to do it, if you’re not a troll.
But I’m not going to accept being blamed for it any longer. I didn’t choose to muddy the waters, because I didn’t choose to make you say that we’re talking about eggs, or that we’re not talking about base 10. You haven’t had this conversation in good faith, and I don’t think you ever will.