Numbers start at one, change my mind

punos

If i place the print statement before the count (rocks += 1) then:

rocks = 0
while rocks < 2:
    print(rocks)
    rocks += 1

output = [0, 1] # incorrect output

rocks = 1
while rocks < 2:
    print(rocks)
    rocks += 1

output = [1] # incorrect output

Both counting loops result in incorrect counts. The logic is that one should state the count after it is made, not before. Yes, it is context-dependent. When the context is counting rocks, then obviously the first loop i wrote is correct because it correlates with the results we get when we naturally count for ourselves. This is not the case for the other counting loops.

Dawnstorm

↪punos

Yeah, I made a mistake, there. Either "< 3" or "<= 2" (if there's such an operation in python, which I don't know) instead of "<2".

When the context is counting rocks, then obviously the first loop i wrote is correct because it correlates with the results we get when we naturally count for ourselves. — punos

Makes perfect sense to me, except I'm not sure about the "obviously".

I mean the original question, in the context of your post, could be read as if I count 2 rocks do I count from 0 to 2 or from 1 to 2. Surely I can translate either of that into a program? I just tinker with the numbers and/or operators, and the order of operations until I get what I want.

punos

if I count 2 rocks do I count from 0 to 2 or from 1 to 2 — Dawnstorm

I think of it like this: before i count, i place my finger on 0 in the number line, and when i make my first count, i move my finger to 1 on the number line, and so on. That 0 tells me what i have before i start counting. If i place my finger at 1 on the number line before counting, then for my first count, my finger moves to number 2 on the number line. That 1 tells me what i had before i started counting. So the process of counting is adding to the prior count. Sometimes that count is 0 (no count), and sometimes it's more than 0.

(< 3) and (<= 2) are essentially the same in the context of the counting loop. Let's try (<= 2):

With print statement before the count:

rocks = 0
while rocks <= 2:
    print(rocks)
    rocks += 1

output = [0, 1, 2] # incorrect output

rocks = 1
while rocks <= 2:
    print(rocks)
    rocks += 1

output = [1, 2] # correct output

In this second counting loop, the number of rocks you start with is already 1, and you are printing your first "count" without having counted yet. So, the loop actually just counts 1 time to get to 2. Although the output is apparently correct, the logic behind the count is not. The loop would function as an accurate rock counter nonetheless.

With print statement after the count:

rocks = 0
while rocks <= 2:
    rocks += 1
    print(rocks)

output = [1, 2, 3] # incorrect output

rocks = 1
while rocks <= 2:
    rocks += 1
    print(rocks)

output = [2, 3] # incorrect output

The reason i place the print statement inside these loops is so that we can see the process of counting as it happens. If i place the print statement outside the loop after it is done counting, then the result will be the same for both counting loops.

rocks = 0
while rocks < 2:
    rocks += 1

print(rocks)

output = [2] # correct final output

rocks = 1
while rocks < 2:
    rocks += 1

print(rocks)

output = [2] # correct final output

punos

↪Dawnstorm

Another way to understand why one must start counting from 0 to count correctly:

Let us assume that we already have a count of 2 rocks. Instead of counting up to 2, we will count down 2 times (the number of rocks we have). Beginning at 2, we discount 1, leaving 1. Then, we count down 1 more time, and we reach 0. A down count of 2 brings us to 0. If we want to get back to 2, we count up 2 times (an equal and opposite operation) from 0 to 1 to 2.

Where you begin counting, and the first count are two different things. They are not the same. Everyone counts this way, but not everyone realizes they are starting from 0.

Dawnstorm

Where you begin counting, and the first count are two different things. They are not the same. Everyone counts this way, but not everyone realizes they are starting from 0. — punos

I just want to say that I find these last two posts very interesting, but I'm not sure I fully understand. I just deleted a post of mine (before posting) where I noticed I talked past the problem while nearly done.

My hunch is whether where you begin counting and the first count are two different things depends on how you model counting, and which model you use depends on what you what you want from the model.

Frankly, counting models that do not start at zero are very counter-intuitive for me, and the last time I thought about things like counting is - what - 20 years ago? (More like 25 come to think of it; time flies whether you're having fun or not...)

I mean if the number of rocks is a variable, and I want to compare the variable over time or space, I'd definitely use a zero-starting point.

But if for some weird reason I want to count a given number of rocks just to align them on an ordinal scale with one rock per category (this is the first rock I counted; this is the second rock I counted...) I would have no zero point. I have no idea why I'd want to do something like that, but then I just find the idea of "numbers starting" weird to begin with, so... why not?

punos

counting models that do not start at zero are very counter-intuitive for me — Dawnstorm

As they should be.

It's not the numbers that start; it's the counting (an action that can start and end). Counting starts at either 0 or the last count result, but 0 is not a number that represents a count, which is why you don't need it to represent a counted item. Your first count is 1, and thus your first represented count starts with 1.

Perhaps it would be helpful to think about what you are counting as the space between the numbers. For example, 1 = (0 to 1), 2 = (1 to 2), 3 = (2 to 3), where each number represents the full space between one number and the next. Instead of counting points on a number line, you are counting spaces (or distances) between the numbers. Both ways work, but the latter method shows you what you are counting as represented by the spaces in between. Consider what your count would be if you had 2.5 items? Is it 2 or 3 or 2.5? Just something to think about.

Knowing any of this is unnecessary for the average person, but as a philosopher or someone who wants to know the truth of things, this model i believe provides the most insight into what is actually happening when we count.

My model for counting can be represented simply as:

x = 0 (or the sum of the prior count)
x + 1 = 1 (x = 1) # count 1
x + 1 = 2 (x = 2) # count 2
...

This, in my view, is the most basic and universal model (algorithm) for counting, and any other model is either derivative or a simplification of this model. My (preferred) counting model yields an accurate count in any case you might apply it to, with the only modification, if necessary, being to the initial condition or quantity. Other models may work fine in some cases but not in all cases.

Zolenskify

↪Fooloso4

Well this too is... unexpected, but appreciated greatly. Thank you for the compliment.

Zolenskify

↪Michael

Well I really think you're wrong.

Zolenskify

but a 0th rock does not exist
— Zolenskify

Saying someone has 0 rocks is not the same as "there is a 0th rock" — one is a nonsensical statement, the other is not. There is a difference between cardinal and ordinal numbers — I learned that in my first year of school.

Well, I don't know your personal life, or where or when you went to school. But I can appreciate you wanting to share that information with me. I see the appeal to online discussion forms, and the advantages of being social to complete strangers; some of us are just unconfident in ourselves, but I promise you it is only temporary, things will get better with enough patience and experience. So, I see where you are coming from and, again, I appreciate your opening up to me like that.

"if I am a sea turtle, then I am Bill Gates (or [insert favorite billionaire])."

We certainly could make this argument, it's not wrong, but anyone who wishes to entertain this would be wasting time
— Zolenskify

No we couldn't, it is wrong. Bill Gates and a sea turtle are mutually exclusive.

Well remember, that is just the way you see things. But like I said, if you want to entertain the argument, I am open to it.

If I am a sea turtle, then there exists any number of abstract realities in which anything we want to happen, can happen. Because we are starting the premise off with a statement that is strictly hypothetical, then any conclusions that follow are also hypothetical, and can be totally imaginary if want them to. For instance, if you had decent taste, then I am the Mad Hatter. As such, I can go an do all sorts of things the Mad Hatter does, like, say, enjoying a tea party. In fact, here is a whole list of things that I could now go an do: https://facts.net/lifestyle/entertainment/17-facts-about-mad-hatter-alice-in-wonderland/#:~:text=In%20Wonderland%2C%20the%20Mad%20Hatter,clock%2C%20always%20on%20an%20unbirthday. Further, I would be portrayed by Johnny Depp in the movie "Alice in Wonderland," 2010. And in this situation, it is a deep honor to be portrayed by such an esteemed artist and actor. But either way, the premise is hypothetical, so the follow up to that is inconsequential; so, no Johnny Depp sadly.

really take some time and educate yourself on the various domains, genus', orders, etc, of the species before jumping to any sort of conclusions here
— Zolenskify

I don't think I need to educate myself on grade school biology, thanks.

You're welcome, but I really think you're wrong here. A well-rounded understanding of the natural sciences is important for any thinker to be able to carry themselves in a sound manner. But, you are free to disagree if you want.

At any rate, I think it agreeable to say that we should come prepared for any sort of discussion, as to not waste time on preliminary information. Just a thought, it may serve you in the future.
— Zolenskify

There is no discussion, you started a thread with a claim that no mathematician will entertain — because first of all, what does the phrase "numbers start" even mean? You used an analogy which relies on the semantics of the English language to prove your claim and I showed another analogy using English that makes the contrary claim. Your OP does not even fulfill criterion B on how to make a new thread.

You are conflating counting (which assumes some existential statement) and mathematics, those two are not the same¹. Overall, another horrible thread by someone who did not research the topic they are starting. Here, have fun: https://web.math.ucsb.edu/~padraic/ucsb_2014_15/ccs_proofs_f2014/ccs_proofs_f2014_lecture4.pdf

1: Don't reply to this with a cut-off quotation that says "Mathematics is the study of counting", read the rest of the quote.

First off, I couldn't agree more. That's pretty much the exact reason why I believe you're here too, entertaining this discussion. Not withstanding, your definition of a mathematician can only be so accurate, considering your knowledge of natural sciences. So, I really can't be asked to take everything you say to heart. But I do see your point, mathematics can too be entertaining, in very much the same way as, say, grade school biology. It just depends on how much we are willing to sacrifice to learn to the topic. Anyways, I don't know how often you come across dictionaries, but either way you put it, we are conversing on a forum, you know, the place where discussions happen. Now, whether or not your arguments within these discussions are grounded in reality is another story.

At any rate, I don't see how your logic is any less "non-sensical" than mine. By your logic, before I pick up anything I have 0 of it. In that case, I technically have, in my possession, every conceivable object in the known universe and beyond - only I have 0 of them; and well, that's just too much for anyone, let alone one unversed in the natural sciences to handle. Nonetheless, I thank you for the thoughts, I will think deeply on these. — Lionino

Lionino

Well, I don't know your personal life, or where or when you went to school.

It is not a fact of my personal life. It is a fact of anyone who went to a functioning school that cardinal numbers and ordinal numbers are different.

You're welcome, but I really think you're wrong here. A well-rounded understanding of the natural sciences is important for any thinker to be able to carry themselves in a sound manner. But, you are free to disagree if you want.

I don't disagree. I have college level education in natural sciences. You however think that the classification of living beings into genus, class, order is something not obvious to everyone clearly because you did not have basic schooling — again you don't know the difference between cardinal and ordinal numbers. You are like a kid who found out about the colour wheel and think he made some grand discovery.

That's pretty much the exact reason why I believe you're here too, entertaining this discussion.

I am not entertaining anything, I am shutting your nonsense down. I debunked your pseudo-argument in the OP and you haven't been able to make a single coherent reply ever since.

Not withstanding, your definition of a mathematician can only be so accurate, considering your knowledge of natural sciences.

Everyone knows what a mathematician is. Again, the fact that you think this is a complex subject is not because it is a complex subject, but because you have the same education as a grade schooler.

I technically have, in my possession, every conceivable object in the known universe and beyond - only I have 0 of them

Yes, that is how it works. You have 0 of everything you don't have. That is a very basic sentence with very basic logic.

I will think deeply on these

You don't think at all, LSD fried your brain.

And good job on the messed up quotations, highlighting and clicking a button is indeed very hard for people with IQ in the single digits.

Zolenskify

↪punos

In this context counting physical objects like rocks can be a bit confusing to some because it's not always clear what exactly is being counted. On the other hand, counting time is more straightforward.

For example, when counting days, day 1 is considered at the end of the day, with the beginning of that day being counted as 0 and ending with count 1. The next day begins at 1 and ends at count 2. Therefore, 1 is the first complete count, but for this to be true, the count must begin at 0. — punos

An interesting note, but in respect to time, things get really blurry really fast. I will be honest, I do not follow how this differs from my example, only that you now add the condition that the beginning of the day is 0. I'm thinking something along the lines of this: we can assign the start of the day at zero, but it is once an interval of time has passed, we now have one; which this is the crux of your argument. But an interval of time is always passing, and can't really be counted in terms of starting and stopping. A stopwatch can do this for practical reasons, but we are then changing what time means because we are now only looking at it in terms of evaluating some other dependent variable. In short, to think about having a start and stop to time kind of makes me want to shoot my self right in the forehead.

When counting rocks, what is actually being counted is the space the rock occupies. This can be seen as the space between 0 and 1 being counted as 1 (the counted entity is contained between 0 and 1). If a rock didn't occupy any space, there would be nothing to count, as there can't be a rock that takes up no space — punos

I will be honest again, I don't follow this thinking either. Say that we are now counting these "spaces" instead of the rocks. That "space" just becomes the object we are counting. So swapping these two objects still allows for my argument to hold. Thank you for these thoughts.

punos

I do not follow how this differs from my example, only that you now add the condition that the beginning of the day is 0. — Zolenskify

This is your example:
"I pick up a rock, I have one rock. Pick up another, have two. Drop them, have none. Only started counting rocks when I picked up the first one. So, numbers start at one."

I would restate your example as:
"I have zero rocks, I pick up a rock, I have one rock. Pick up another, have two. Drop one and I have one, drop that one and I have zero, right back where I started."

But an interval of time is always passing, and can't really be counted in terms of starting and stopping. — Zolenskify

It is not time itself that stops or starts; it is you who starts counting and then stops. You are not trying to count all of time, which is infinite and thus impossible, but just the duration (temporal space or distance) of some finite phenomena. A count result can be defined as how many 'times' (time) a single count was made. Counting is an activity, which means it has a temporal dimension.

A stopwatch can do this for practical reasons, but we are then changing what time means because we are now only looking at it in terms of evaluating some other dependent variable. — Zolenskify

I don't see how the meaning of time changes when we count cycles of time. What do you mean by dependent variable in this context?

Say that we are now counting these "spaces" instead of the rocks. That "space" just becomes the object we are counting. — Zolenskify

That is precisely what i am suggesting as a representational placeholder for any object being counted. It's not a rule, but i find that conceptualizing it this way affords me a more accurate way of understanding what is happening when counting happens. There is, in any way you think about it, a kind of separation between numbers, or if not, then we would not have numbers. I think it is a more rigorous way of thinking about numbers, anchoring the concept of numbers closer to our physical experience of the world in a spatial sense.

So swapping these two objects still allows for my argument to hold. Thank you for these thoughts. — Zolenskify

For your argument to hold i believe it needs to start from 0 in order for the first count to be 1.

You're welcome, and thank you as well for your thoughts.

Zolenskify

I think you read way more into my saying that I can't change your mind. It was not meant as a comment on the openness of you and your question, and it was not a comment my own abilities; it was a comment on the nature of numbers and the number 1. By saying "it's too, late" I meant that we've already started using numbers, and when we started, we were at "1". — Fire Ologist

Well this would mean that the premise on which I based my observation was totally unfounded.

I just meant it makes sense to me that 1 has to be the first number. I gave my arguments for that to demonstrate my first impression of the question you've raised. So far, I can't change my own mind, so I can't argue something that might change your mind. And I don't yet see there is any reason to think differently. Not yet, but I'm open to it. — Fire Ologist

I think what we have here is an agreement.

The best summary of my thinking here is the notion of starting. If we are asking a question about a start, about starting something, like numbers, we are already in a position only to say "1", first. We can't start with anything else but the first, which numerically, is "1". — Fire Ologist

I see what you mean.

Because "1" is built into starting something, I don't see how to argue anything else but "1". — Fire Ologist

Beautiful.

Zolenskify

"Counting" may start at 1. Numbers, however, do not "start" (i.e. begin / end). — 180 Proof

↪180 Proof

I think you ought to spend more time in Singapore.

Zolenskify

Every computer programmer knows that counting begins at 0. — punos

↪punos

Maybe... But I want to know what you think.

Zolenskify

programmatically in Python:

rocks = 0 # beginning at 0
while rocks < 2:
rocks += 1
print(rocks)

output = [1, 2] # correct output

rocks = 1 # beginning at 1
while rocks < 2:
rocks += 1
print(rocks)

output = [2] # incorrect output — punos

Well, what I see here is that you are saying 1+1 is not 2. So I don't know where you're coming from.

Zolenskify

This is not to say I do not have an ego, I certainly do, but I can cope with being wrong at times in a much better way than others it seems.
— Zolenskify

The only person here who ever said anything about "ego" was you. People replied to your poorly-made OP and you went on a rant like you were deeply hurt. Did you take LSD and suddenly made up your mind that you are enlightened? Because you are not. — Lionino

All this talk about enlightenment. What the hell are we doing here then?

punos

But I want to know what you think. — Zolenskify

I believe that is what i've been doing.

punos

programmatically in Python:

rocks = 0 # beginning at 0
while rocks < 2:
rocks += 1
print(rocks)

output = [1, 2] # correct output

rocks = 1 # beginning at 1
while rocks < 2:
rocks += 1
print(rocks)

output = [2] # incorrect output — punos

Well, what I see here is that you are saying 1+1 is not 2. So I don't know where you're coming from. — Zolenskify

In the first example, since it is starting from a value of 0, it enters the counting loop one time, adding 1 to 0 (0+1=1). Then it enters the loop again and adds 1 a second time to the last value result [1], updating the count result to [2]. This is why the first example has an output of two numbers [1, 2], because it counted twice.

In the second counting loop example, since the starting value is already 1 before the first count, the loop simply counts 1 time, resulting in one count of [2]. This loop added 1 to 1 (1+1=2), resulting in a value of [2]. That is why you only see one number as the output result [2], because it only counted one time.

In both cases, 1 + 1 = 2, but what you are neglecting to see is that the true operation was 0 + 1 = 1 (first count), and 1 + 1 = 2 (second count).

I'm coming from 0. That's where i'm coming from.

Zolenskify

[insert a well-rounded, and logical argument here]

... Great, now I really don't know what I think anymore. — Fire Ologist

Indeed, my friend, we have reached the pinnacle of thinking: which is not thinking.

punos

↪Zolenskify

Let me provide another, but different illustration that shows why counting and even numbers themselves begin at 0. Consider the two following number sequences and their logical progression:

Sequence A:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
10, 11, 12, 13, 14, 15, 16, 17, 18, 19

Sequence B:
1, 2, 3, 4, 5, 6, 7, 8, 9
11, 12, 13, 14, 15, 16, 17, 18, 19

Questions:
Which one of the above number sequences is correct, and which one is incorrect, and why?
What numbers are missing and why?
What is the relationship of the number 10 to the number 0?

Fire Ologist

↪Zolenskify

"The answer to the ultimate question is..........................42."

punos

"The answer to the ultimate question is..........................42." — Fire Ologist

Perhaps the question to the ultimate answer is ..................... 2 × 3 × 7 = ?

Arne

Numbers start at zero. The counting starts at 1. If I am running a 100 yard race, I do not get to start at yard 1.

punos

I'm sorry to say that the concept of "natural numbers" (counting numbers) should be abolished. It is logically inconsistent and causes confusion as to the true nature of number.

Metaphysician Undercover

When making arguments it is good to have a leg to stand on, to take a stance, and have a proper and I assume in your case fetching attitude. — Fooloso4

But it might be better to have at least one rock in hand, and the will to demonstrate what an active rock can do.

Lionino

What the hell are we doing here then? — Zolenskify

Me? Thinking. You? I genuinely don't know, I'm not a psychologist.

Numbers start at one, change my mind

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