Numbers start at one, change my mind
Title is what it sounds like. 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.
Comments (57)
Before you picked up a rock, you had 0 rocks. So, numbers start at 0. :roll:
Here are some interesting sources on these classifications that I mentioned; even as someone who isn't totally versed in the field, I found these to be quite thought-provoking:
(1) Source 1
(2) Source 2
First, there are no numbers. We don't just find numerical representations with our senses. We form them. Now that we've formed them, there are numbers. You pick up a rock, and you call it 1 (whether it is one or is not , maybe it's a rock with some moss on it and dirt, whatever, you pick it up and construct the basis of math by calling it "1"). You've made the first number.
You can't make two half rocks without the first rock. You don't name something a half, first. You have to have a whole before something can later be called half of that whole. By saying "half" you already referred to a whole. Halves come after wholes, not before they are made whole.
And you don't start with zero. We can't recognize zero until we recognize one. You learn and name zero by mentally removing the one rock or all of the rocks and things. Zero comes after 1 in experience, but is placed before one on the number line because of logic (mental functioning, just like naming something "one" or conceiving of "half-ones".)
There is no such thing as a negative rock. Negatives are mental constructs. Now that we have a new mental object we call "1" we can build off of it in all directions and build functions that yield zeros, twos, negative thirty-fives, the infinite.
The concept of "one" is the only that might have a referent in a world where you could make any start, such as the start of numbering things. Two rocks don't exist without a mind making a set called "two" having "rocks" as its members.
We certainly could make this argument, it's not wrong, but anyone who wishes to entertain this would be wasting time; as if there isn't enough of that happening already. We could go on all day about what the world would be like if I were a sea turtle (or any other member of the Cheloniidae family; some information can be found here: https://phys.org/news/2015-11-insights-family-tree-modern-turtles.html; 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; we could split hairs, but there are distinct differences), and have a hell of a time doing it. But I'm not a sea turtle, I'm a person. So, these arguments don't really matter.
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.
@Vaskane made a similar argument. But theirs's too was besides the point, as they failed to ground their definition of a rock in any sort of reality. At any rate, thank you for the response. This was a viewpoint I had not considered. Cheers!
Correction: Sorry, misread who you had responded to. But still, don't steal things, or at least avoid incriminating yourself in the process...
That is a true issue for physics or metaphysis (identity of a rock), but no matter what the results of those inquiries, even if no results, it could have no impact on the definition of "1". That's the beauty of this math we've invented. Which seems to me, got it's start with some "one".
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.
Quoting Zolenskify
No we couldn't, it is wrong. Bill Gates and a sea turtle are mutually exclusive.
Quoting Zolenskify
I don't think I need to educate myself on grade school biology, thanks.
Quoting 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.
Quoting Vaskane
Subtraction is derived from addition. So numbers would not "start" with a negative number.
I'm just gonna stop you right there: I really think you're wrong. You can change my mind, I just need a strong argument, and it's definitely not too late; I want to see things differently if they make more sense that way. Some people are close minded, but I am open to new ideas. Try to avoid putting yourself down too, especially in an online conversation like ours. I think we can really learn a lot from these sorts of discussions, and someone such as yourself (who I can already see is of an upper echelon of thinking to begin with; less you would not be on "The Philosophy Forum") has a lot to offer it seems. So please, restructure your argument without discrediting yourself; you can do anything you set your mind to.
I do see where you're coming from though. It seems that the world were in is so cut throat, that people take the slightest bit of criticism and form their entire identity around it. Well forget that jazz. As an artist, my ego is demolished on such a frequent basis that it is pretty much part of who I am at this point, and I feel all the better for it. 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.
In other words: Ignore the haters, but still try to recognize the difference between blatant heckling and constructive criticism, because there is a difference.
At any rate, thanks for the response. This too has given me much to think about. And remember, take it easy and just take a minute to breathe; we're honestly all just here to help each other out and grow. But we can't do that if we are constantly holding ourselves to these impossibly high standards, and then blaming ourselves for not reaching them. Someone who I learn a lot from in Andrew Huberman, he has a pretty interesting podcast episode that relates to this that I think you would really benefit from:
https://www.youtube.com/watch?v=x4m_PdFbu-s
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.
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.
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".
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.
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".
Because "1" is built into starting something, I don't see how to argue anything else but "1".
Every computer programmer knows that counting begins at 0.
programmatically in Python:
output = [1, 2] # correct output
output = [2] # incorrect output
This clarifies the question for me.
I was talking about the fact that the first unit ever made in a mind, so the first number ever counted, was a "1", and all units since then (yes units), were multiples and divisions of when we first started counting units of one. So quantification started long ago with a 1. 'Numbers start at one' would be a weird way to say it, but it reflects this sense of "start" and "numbers" and "1" I meant.
Quoting Zolenskify
But if the statement 'numbers start at one' means "of all numbers on the number line, numbers start at 1", then maybe it makes sense to say numbers don't start.
The act of counting itself moves in increments of 1. When physically counting, you have to say "1" in some fashion, first. If you count by fours, you first counted 4 ones, to make the first four, so you still started at "1".
However, we might also say we start counting from zero, and for the instant between zero and one, that is our start of counting. The first count, is a "1", but we start counting closer to zero, or at zero.
How about the genealogical-psychological first historical act of counting (way back when caves were still fashionable), the very first count was likely a physical word for "one". Just like our minds first made a unit, and one, to count at all, we made word "one" itself to follow, and then we had to make words for "two" and "three" probably quickly "none" or "zero". The word "one" may have been how numbers started. Maybe.
But now that numbers are here, however they started, we can start counting from any number. The number line gets laid out clearly the same every time; no matter what numbers you start at, it lines up the same. The only place we might find to "start" the number line, would be zero. There is a logic to it, a symmetry.
So it looks like four senses.
1. At the first moment quantification occurred to a mind, the number "1", the unit, had to be there first. Unitizing is the birth of all math. Numbers start at one.
2. When starting a count, you can be said to start "at 1" or "from zero" and so there is something unresolved there. Numbers may not start at one.
3. The first cave person who ever tried to count out loud, probably said and meant the word "one". Numbers start with one. (Who knows, throws in some actual skin in the game).
4. The most logical place to position the number line is from zero, but it can start from anywhere. So numbers don't start and if you had to choose, you would choose zero.
And what about lists? Has anyone ever started a list with anything, ever, besides 1? Put "Lists start with one" up there on my list, somewhere between 2 and 3.
Great, now I really don't know what I think anymore.
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.
There is nothing correct or incorrect about the output, it is just the way you programmed it and how Python works.
Quoting Fire Ologist
That is somewhat productively discussed in the Postmodernism and Mathematics thread.
What is your criteria for correct or incorrect? Are you saying it doesn't matter how i program it, that i can choose either one, and it'll be as good as anything else? If that is the case then it would appears that no one is correct or incorrect about anything, because it is just the way they said something. Really?
In the ancient Greek concept of number the first number is two. One is the unit of the count, what it is that is being counted. We see this here:
Quoting Zolenskify
The number of igneous rocks is not the same as the number of sedimentary rocks. To answer the question "how many" we need to know how many what.
I simply told the program to count 2 rocks, and yes, i told one to start from 0 and the other to start from 1. If you look closely, you will notice the two code examples are identical except for the starting or initial condition.
You are correct in that both code samples are logically correct in their execution, but as in logic, one began with a different 'premise' than the other. And we know that if you have an incorrect premise, then your conclusion would be incorrect no matter how flawless the execution of the logic.
The two code samples illustrate what happens when you start your count from 0 versus 1. Both cannot be correct for use in counting rocks.
Here is ChatGPT:
which one of these code examples is the correct one for counting rocks?
The first code example is the correct one for counting rocks. It initializes the variable "rocks" to 0 and then uses a while loop to increment the value of "rocks" until it reaches 2, printing the current value of "rocks" in each iteration. The output of this code is "1, 2." Here's the breakdown of the code:
This code will output:
1
2
The second code example initializes the variable "rocks" to 1 and then uses a while loop to increment the value of "rocks" until it reaches 2, printing the current value of "rocks" in each iteration. The output of this code is "2," which is not the correct one for counting rocks.
Also, notice that the output count did not include 0, although it's where it began counting. We forget 0 because it's usually invisible as our reference point before a count can begin. When you count, what you are doing is adding to 0, and you must start at 0, or your count will be off by the number that you started counting from.
Sure. But the programming language does not "know" that counting start at 1 for some languages the first element of a list has index 0, in other languages index 1. And the fact that one piece of code counts "correctly" and the other "incorrectly" (like ChatGPT says) begs the question as to why one is right and the other wrong, which is the thread's topic.
The relevance lies in the logic, not the programming language. There is a right and a wrong way to count. When counting rocks, it is essential to establish whether there are already rocks present. If i have 2 rocks and then pick up and count another rock, i will have 3 rocks (the count begins at 2). Conversely, if i don't have any rocks and then pick up and count 1 rock, i will have just 1 rock (the count begins at 0).
I have never used MATLAB, so i can't comment on what it's doing. If you have a code snippet that i can look at, that would be helpful. MATLAB isn't a general-purpose programming language, but if MATLAB uses 1 as its base index, it must mean that it doesn't represent a count until the first count is made. In Python, the count begins at 0 before the first count is made. I'm sure that MATLAB uses a 0-based index under the hood and creates a 1-based index after the first count.
Quoting Lionino
The reason one is right and the other is wrong is that one starts from 0 and the other starts from 1. If i wanted to count rocks with an app that uses the example code that starts with one, then my app would count rocks incorrectly. It's just that simple to verify, like counting horse teeth.
For instance, my "workout" is pretty much comprised of cardio and legs only, that is, skateboarding. My upper body is quite thin (on this note, I would prefer to keep a lean build versus gaining any weight, I don't want to sink my surfboard, for when I do that instead of skating). I would compare my body type to a correctly-oriented pyramid; a stark contrast to what we typically see, the "upside down" pyramid, where you have these (albeit very kind and educated) fellows with massive upper bodies but are supported by two chop sticks. I am very much the opposite, and am okay with that. In fact, my legs are like works of art. In ancient Greece, I would hedge my bet that I would be worth sculpting in some capacity. Now, what type of rock the sculptor will choose for this endeavor, I don't know. But, if I had to guess, I would say perhaps igneous; although you seem to have something against this variety. Nonetheless, here is an article I found on various sculpting materials: https://www.britannica.com/art/sculpture/Materials and here they consider something I had not even thought about: stone. Which this completely changes the dynamic of the whole damn argument if you really wanted to go there.
But staying on topic, there is but one rock that is actually quite active. As we know, Dwayne "The Rock" Johnson is anything but sedentary, and he actually has more of a figure of what I was referring to. At least, that is just my opinion on things, and is not the end-all-be-all way of seeing the world. But thank you for your comment anyhow, I will think on this.
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.
You're half right.
Well, when you wrote that program that's how you interpret "counting". You chose not include the initial value in the count; if you'd performed the print operation before the adding operation you'd get [0,1,2] and [1,2] (correct me if I'm wrong; I don't know python).
I really don't see a logical difference. Either one's fine. (In specific contexts one might be more efficient than the other, though.) Basically, you can have either initial value for the desired output; you just have to switch the operations around.
If i place the print statement before the count (rocks += 1) then:
output = [0, 1] # incorrect output
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.
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".
Quoting 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.
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:
output = [0, 1, 2] # incorrect output
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:
output = [1, 2, 3] # incorrect output
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.
output = [2] # correct final output
output = [2] # correct final output
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.
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?
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
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.
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.
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.
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.
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.
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.
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.
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.
Quoting 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.
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."
Quoting 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.
Quoting 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?
Quoting 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.
Quoting 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.
Well this would mean that the premise on which I based my observation was totally unfounded.
Quoting Fire Ologist
I think what we have here is an agreement.
Quoting Fire Ologist
I see what you mean.
Quoting Fire Ologist
Beautiful.
I think you ought to spend more time in Singapore.
Maybe... But I want to know what you think.
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.
All this talk about enlightenment. What the hell are we doing here then?
I believe that is what i've been doing.
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.
Indeed, my friend, we have reached the pinnacle of thinking: which is not thinking.
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?
"The answer to the ultimate question is..........................42."
Perhaps the question to the ultimate answer is ..................... 2 × 3 × 7 = ?
But it might be better to have at least one rock in hand, and the will to demonstrate what an active rock can do.
Me? Thinking. You? I genuinely don't know, I'm not a psychologist.