1 divided by 3 revisited

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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 4:03 pm

Flannel Jesus wrote:> Then why bring up some other base when you didn't think I was using another base

I didn't bring it up because of what you were or weren't using. I brought it up of my own volition, for my own reasons. Please read the place in the conversation where I brought up another base - read it carefully, and try to understand that I was not even remotely implying that you were using any other base.

I was using another base. I made a choice to use another base. Not you. I made that choice, I made it clear that I was making that choice, I even made it clear why I was using that base.


Base 6 is not part of this conversation, so please refrain from using any other base in this part of the conversation, it just muddies the water.

For right now, we are using base 10.

12 Eggs is this many - 0 0 0 0 0 0 0 0 0 0 0 0
1 Dozen is this many - 0

We have already agreed that 12 eggs can be divided into 3 equal parts, each part having 4 eggs.

We are now talking about 1 Dozen.

Can 1 Dozen be divided into 3 equal parts? Yes or No?
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 4:27 pm

> Base 6 is not part of this conversation, so please refrain from using any other base in this part of the conversation, it just muddies the water.

No concept is part of a conversation until it is. If one of us decides that some particular concept is important to bring up for a point, then we'll bring it up. If you decide to change the object of division from "eggs" to "chickens", I'm not going to oppose that on the grounds that it's "not part of the conversation". That's not fair, I don't accept that you have the right to unilaterally decide what is or isn't part of the conversation.

At the beginning of the conversation, percents weren't part of the conversation. And then you brought up percents. I didn't particularly like that you brought up percents, but I didn't complain about it either. You're allowed to bring up concepts you think are relevant to the conversation, and it would be acting in bad faith for me to disallow that.

If you're making a claim specifically about base 10, and nothing outside of base 10, then you would possibly have grounds to tell me not to bring up other bases. But we've established that your claim isn't about base 10, and since it's not about base 10, if I have a relevant point to make that uses another base, I'm going to make that point using another base. I don't agree to you having a monopoly on the parameters of the conversation - you can have a monopoly on defining the parameters of your own claims, but I will not just acquiesce and give you the right to determine what points I am and am not allowed to make. That is NOT the structure of a good faith discussion.

> Can 1 Dozen be divided into 3 equal parts? Yes or No?

Yes I think so.
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 4:37 pm

Flannel Jesus wrote:
Yes I think so.


In base 10 (which I am using and speaking about) "One" or "1.00" or "100%" are all the same thing. There is no difference. "One" is a word for "1.0", and 1.0 literally is 1.00, which is literally 100 Hundredths, which is 100%.

That is a totally different animal than changing bases. Nothing is changed between "One", "1.00", or "100%", they all mean EXACTLY the same thing mathematically.

But as you have already acknowledged, in base 3 "10" is this many - 0 0 0

See the difference?

When I say "12" I am speaking about this many "0 0 0 0 0 0 0 0 0 0 0 0"

In base 3 "12" is this many "0 0 0 0 0"

To try to confuse the issue by switching bases is a dishonest tactic. We are speaking about this "0 0 0 0 0 0 0 0 0 0 0 0" not this "0 0 0 0 0"

Got it?

You think you can divide 1 dozen (this many "0") into 3 equal parts (this many parts "0 0 0") so explain in detail.

I want to know HOW MANY percent each part is, and I want to know HOW MANY dozen each part is?

Explain in simple terms using base 10.
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 4:53 pm

It's not my aim to confuse by switching bases, nor is it dishonest, it's literally Central to my entire point of view on this conversation. You knew that coming in. There's nothing inherently dishonest about disagreeing with you on this basis, when you say that your point is not ABOUT base 10 but that it merely uses base 10. It's not dishonest, I'm not tricking you, I am upfront about it. This is my point and you know it's my point.

My view is,

a) there's no reason to prefer one base over another

b) 1/3 is perfectly representable in radix point form in other bases, so

c) 1/3 therefore shouldn't be viewed to have the problems you think it has.

The only problems you can demonstrate with 1/3 are problems in base 10. I do not believe that base 10 is a fundamental part of reality, that it takes precedence over other bases. That's precisely why I disagree with your claim. There's nothing dishonest about my take. It is entirely honest. You may disagree with it, but it is not dishonest.

If you don't want to engage with this point of view, you don't have to. We can quit here. But this is my point of view, this is what you signed up for. If you only signed up for the express purpose to tell me "other bases are dishonest" then we've achieved everything we can here. Good job, you've achieved your goal, you showed me. But if that's why you joined the conversation, then you've broken the agreement at the center of this conversation, because it wasn't begun in good faith from your side.

If you did intend to talk in good faith, on the other hand, then you know this is my point of view, and so you'll either engage with it, or end the conversation.

I've laid out my premises for my point of view. If your claim about 1/3 is not merely a claim about base 10, then I invite you to engage with my point of view honestly.
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 5:01 pm

You said you think you can divide 1 Dozen into 3 equal parts in base 10. Where is your explanation?

We can talk about other bases after we conclude base 10 conversation. I am not trying to limit the conversation to base 10, only to keep the bases separate, as they should be.

For me to talk about "12" meaning this many 0 0 0 0 0 0 0 0 0 0 0 0 and for you to mix that with base 3 this many 0 0 0 0 0 is just not right.

Stick to base 10 unitl we have agreement, and then move on to a different base and we can discuss that independent of other bases. It is insanity to try to mix bases speaking about 0 0 0 0 0 0 0 0 0 0 0 0.

Why would you want such muddy water when trying to get to clarity on base 10?

Again, you said you think you can divide 1 dozen into 3 equal parts, so let's hear it.
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 5:03 pm

(1 Dozen) / 3, that's how you do it
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 5:04 pm

Flannel Jesus wrote:(1 Dozen) / 3, that's how you do it


How many dozen is each part?
How many % is each part?
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 5:05 pm

100/3 percent, 1/3 dozen
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 5:14 pm

Flannel Jesus wrote:100/3 percent, 1/3 dozen


Do you know what I mean when I ask "how many?" I mean I want to know a number.

Say there are some apples on a table. I ask you how many apples are there. You respond with a number, right? You respond with something like "there are 12 apples on the table." You don't respond with the fraction 12/1.
"How many" is a word, like "twelve." It is not a fraction. Do you count 1/1, 2/1, 3/1, 4/1, 5/1??? or do you count 1,2,3,4,5??

Now I am asking you HOW MANY (a number, not a fraction) dozen, and how many %.
If you must use a fraction for %, then I am asking you how many Hundredths is each part. An example would be 25/100 for 4 equal parts of .25 dozen each.
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 5:25 pm

At the beginning of the thread, we had this discussion. I clarified that I don't agree with you that fractions are not numbers, and that some fractions are not representable in base 10 as finite decimals, but are only able to be approximated by such notation.

My position on those things has not changed. You can approximate 1/3 as .3333... , But 1/3 itself is an acceptable answer as far as I'm concerned.
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 5:29 pm

Flannel Jesus wrote:At the beginning of the thread, we had this discussion. I clarified that I don't agree with you that fractions are not numbers, and that some fractions are not representable in base 10 as finite decimals, but are only able to be approximated by such notation.

My position on those things has not changed. You can approximate 1/3 as .3333... , But 1/3 itself is an acceptable answer as far as I'm concerned.


Let's magnify the situation so we can see clearly what is going on.

Let's try to divide 10 eggs into 3 equal parts. The first step is easy, each part has 3 eggs, and there is 1 remaining egg. So 4 parts so far, 3-3 and 1-1, for a total of 10 eggs. Agreed?

So we have 4 parts so far, 3 parts are equal, and the other part is not like the others. Agreed so far?
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 5:31 pm

Yeah that looks fine so far
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 5:35 pm

Flannel Jesus wrote:Yeah that looks fine so far


Good. So now all we have to do is divide the remaining 1.0 (100%) egg into 3 equal parts. Again, 30% for each of the 3 parts totaling 90%, with a remaining 10%.

So now we still have 4 parts, 3 of which are equal at 3.3 eggs (totaling 9.9 eggs) and the other oddball part that is .1 egg. Grand total 10 eggs (9.9 + .1)

Agreed so far that there is still 4 parts?
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 5:39 pm

I agree that the way you've split it leaves it with those groupings, yeah.

I don't know why you're splitting it like that though, why not split the last egg into 3 equal pieces?
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 5:43 pm

Flannel Jesus wrote:I agree that the way you've split it leaves it with those groupings, yeah.

I don't know why you're splitting it like that though, why not split the last egg into 3 equal pieces?

You can not split 100% into 3 equal parts, that is why the first split was 3 eggs for each part with 1 remaining part. If you could split it into 3 equal parts it would go no further than the first split.

Why didn't you ask why I just didn't split it into 3 equal parts at the beginning, because you know 3 x 3 =9, not 10? because you know 3.3 x 3 = 9.9?? Because you know 3.33 x 3 = 9.99?? and on and on?

We literally have 10 eggs, and the first split is 3 x 3 with a remaining 1. Now the division tries to finish by dividing that 1 into 3, which again means 90% and 10% left over. That goes on INFINITELY, so 10 eggs can't be split into 3 equal parts.
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 5:47 pm

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?
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 5:55 pm

Flannel Jesus wrote: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)
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 6:03 pm

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?
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 6:16 pm

Flannel Jesus wrote: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.


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.

Flannel Jesus wrote: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 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.
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 6:27 pm

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.
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 7:06 pm

Flannel Jesus wrote:
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.
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 7:10 pm

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.
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 7:11 pm

Flannel Jesus wrote: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.


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?
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Re: 1 divided by 3 revisited

Postby Motor Daddy » Tue May 31, 2022 7:14 pm

Flannel Jesus wrote: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.


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.
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Re: 1 divided by 3 revisited

Postby Flannel Jesus » Tue May 31, 2022 7:19 pm

> 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
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