Comments

  • What are you listening to right now?
    Matthew Halsall and The Gondwana Orchestra - Journey in Satchidananda


    Matthew Halsall - Daan Park


    Matthew Halsall - Samatha (Poetree Remix)


    Matthew Halsall and The Gondwana Orchestra - Kiyomizu-Dera
  • Numbers start at one, change my mind
    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.
  • Numbers start at one, change my mind
    "The answer to the ultimate question is..........................42." — Fire Ologist

    Perhaps the question to the ultimate answer is ..................... 2 × 3 × 7 = ?
  • Numbers start at one, change my mind
    ↪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?
  • Numbers start at one, change my mind
    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.
  • Numbers start at one, change my mind
    But I want to know what you think. — Zolenskify

    I believe that is what i've been doing.
  • Numbers start at one, change my mind
    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.
  • A Dialogue about Sweaty Socks, a Huge Bag and Everything
  • Should I become a professional roller skater?
    ↪an-salad

    If roller skating is your only option, then you should probably pursue it, but you should also consider other proximally interesting options. You might want to have a non-athletic career as a backup in case you get injured in a way that prevents you from continuing a skating career.

    Additionally, you should think about the possibility of AI robots taking over the sport in the near future. With rapid recent advancements in deep-skate network architecture, human skaters may soon become altogether obsolete in the sport of roller skating.

    > end transmission
    > exit code 1
  • Numbers start at one, change my mind
    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.
  • Numbers start at one, change my mind
    ↪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.
  • Numbers start at one, change my mind
    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
  • Numbers start at one, change my mind
    ↪Dawnstorm

    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.
  • Numbers start at one, change my mind
    ↪Lionino

    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.

    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. — 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.
  • Numbers start at one, change my mind
    ↪Lionino

    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.
  • Numbers start at one, change my mind
    ↪Lionino

    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:


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

    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.
  • Numbers start at one, change my mind
    There is nothing correct or incorrect about the output, it is just the way you programmed it and how Python works. — Lionino

    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?
  • Numbers start at one, change my mind
    ↪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
  • Numbers start at one, change my mind
    ↪Zolenskify

    Every computer programmer knows that counting begins at 0.
  • Numbers start at one, change my mind
    ↪Zolenskify

    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.
  • What Are You Watching Right Now?
    Just finished watching the series last night, and i do recommend:
  • Proof that infinity does not come in different sizes
    Another:

    Suppose that the universe has infinite space, and let's also say that there is an infinite number of particles in this space. For there to be space between the particles, would that not make space a bigger infinity than the infinite number of particles in the infinite space?
  • Proof that infinity does not come in different sizes
    The statement that some infinities are bigger than others comes from set theory. The OP talks about infinities in the context of counting procedures. These are two different concepts of infinity. — DanCoimbra

    Most of what i think about infinities comes from my own intuitions, so forgive me if i sound a bit ignorant of the well-established terms and procedures involved.

    The "counting procedure" aspect is what i relate to the temporal sense of speaking or thinking about it. The other side seems to be more spatial in character, which instantiates an infinity all at once, outside time, so to say. It's just something i noticed recently and thought it might be useful to know when thinking about infinities. There are probably proper terms for these distinctions, and if there aren't then there should be.

    Welcome to TPF! :smile:
  • Proof that infinity does not come in different sizes
    ↪tim wood

    Yea, like i said im not up on all the terminology. I'm a little bit motivated now to look a little deeper into it, because i do find it interesting. I'm going to look up some of these concepts you mentioned like transfinite cardinals, and ordinal arithmetic. But i'd like to ask.

    What was i describing in my last example about the infinite hotel. What is the correct terminology for what i described?
  • Proof that infinity does not come in different sizes
    ↪Michael

    Is it?
  • Proof that infinity does not come in different sizes
    That's not Hilbert's paradox. — Michael

    Yes, i am aware of that, but i didn't see the point in describing something one could just read anywhere. I was trying to show a different way of conceptualizing different sizes of infinities. That's all, but i'm more interested in if my example is a reasonable one or not.
  • Proof that infinity does not come in different sizes
    Another example that just came to mind related to Hilbert's infinite hotel thought experiment.

    Consider a hotel with an infinite number of rooms, all of which are occupied. Due to the infinite guests, there are no vacant rooms. However, if each room in the hotel were to magically double into 2 rooms, the hotel would then have an additional infinity of rooms to accommodate an extra infinity of guests. Although the number of rooms seems the same in both cases, the capacity differs in some sense. In the first case, no more guests can be accommodated, while in the second case, an additional infinity of guests can be accommodated. This doubling (spacial sense) can continue (temporal sense) indefinitely in both time and space.
  • Proof that infinity does not come in different sizes
    If there is no end to something, how can another thing with no end be twice as large as it? Don't they both have no ends? — Philosopher19

    I believe the the concept of infinity is often misunderstood because it can be applied to different contexts, such as time and space, which are not necessarily equivalent. To explore the differences in sizes between different infinities, let's consider a few thought experiments that illustrate how infinity can vary in magnitude.

    First, imagine you have achieved immortality and are presented with two options: to receive $1 every day forever or $1 every year. Intuitively, you would choose $1 every day because, over the same infinite duration, you would accumulate more money. This illustrates that while both options extend to infinity in time, the rate at which you receive money differs, leading to a larger "size" of wealth in one scenario over the other.

    Now, let's consider a spatial analogy. Imagine two pipes, both of infinite length, but one has a diameter of 1 inch and the other has a diameter of 10 inches. Despite their lengths being equally infinite, the pipe with the larger diameter has a greater volume. This demonstrates that even with one dimension being infinite, other finite dimensions can contribute to a difference in "size" or capacity.

    Interestingly, if we were to expand the diameter of the pipe to infinity as well, we would lose the essence of what makes a pipe a pipe. To maintain its identity, certain characteristics, like diameter, must remain finite. This constraint allows us to differentiate between pipes of different diameters, even if their lengths are infinite.

    Lastly, consider an infinite number of pencils, each 6 inches long, laid end to end to form a line of infinite length. If we compare this to another line composed of an infinite number of 3-inch pencils, both lines would stretch to infinity. However, if you were to take one pencil from each line, there would be a clear difference in their lengths. This paradox highlights that while the total lengths of both lines are infinite, the "size" of their components is different, and this difference is observable when comparing individual elements.

    So, the concept of infinity can indeed vary in magnitude depending on the context. Temporal infinity can differ based on the rate or frequency of an event, while spatial infinity can vary when other dimensions are considered. These examples show that not all infinities are created equal, and it is the nuances in their properties that allow us to distinguish between them.
  • Proof that infinity does not come in different sizes
    When considering a sequence of numbers, such as those between 0 and 4, where there are an infinite number of elements (including fractions and irrationals) between 0 and 1 and every other natural number in the sequence, the set of numbers between 0 and 2 would contain more elements than between 0 and 1. If one were to continuously move through this sequence of numbers, they would never reach the number 1 since one would have to move through an infinity of fractions first. In contrast, if the infinite sequence consists simply of natural numbers, reaching 1 would happen almost instantly.

    This comparison illustrates that the "distance" covered between 0 and 1 in the first example is different from the "distance" between 0 and 1 in the last example. It can be concluded that the first example which includes the rationals and irrationals represents a larger infinity than simply an infinite series of natural numbers.

    Does this explanation make sense? I admit that I haven't spent much time studying the intricacies of infinities and am not completely familiar with the technical terms and notations that mathematicians typically use to discuss these concepts.
  • Proof that infinity does not come in different sizes
    ↪Philosopher19

    Yes, if you were to measure both distances at a specific point in time, but outside the context of a finite time measurement, the distance is probably equally infinite for both.

    I think that to make sense of infinities, one has to have a system for extracting their finite properties, as I mentioned in my prior post, or by looking, for example, at the difference between one element in a sequence and the next, which has a specific finite value. This specific value for example can be considered a fundamental component of a periodically regular sequence, by which any periodically regular sequence can be constructed, including infinite ones.
  • Proof that infinity does not come in different sizes
    ↪Philosopher19

    Any infinite sequence is equal in terms of number of elements to any other infinite sequence, but i do not think they are equal in terms of magnitude or value.

    Considering these two infinite sequences:
    sequence 1 = {1, 2, 3, 4, ...}
    sequence 2 = {.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, ...}

    Take for instance the first 4 elements of any 2 infinite sequences, and observe the last number. If the last number of one series is bigger than the last number in the other series then that sequence has a larger magnitude. In this case then sequence 1 is larger in magnitude than sequence 2.

    sequence 1 = {1, 2, 3, 4, ...} = 4
    sequence 2 = {.5, 1, 1.5, 2, ...} = 2

    Therefor sequence 1 is greater than sequence 2 in terms of magnitude or value.

    Alternatively, if one selects two arbitrary numbers that are common to both sequences such as the numbers 1 and 4 then sequence 2 is larger than sequence 1 because more numbers are included by sequence 2 between values 1 and 4.

    sequence 1 = {1, 2, 3, 4, ...} = 4
    sequence 2 = {1, 1.5, 2, 2.5, 3, 3.5, 4, ...} = 7

    Therefor sequence 2 is greater than sequence 1 in terms of magnitudes or values represented. It can be said that sequence 2 has higher resolution than sequence 1.
  • "This sentence is false" - impossible premise
    The first one is the sentence “The sun is yellow”, and the second one is “this sentence is false”. — Skalidris

    This is how i look at it:
    If it is true that the Sun is yellow then the first sentence is a true statement, else it is false regardless of any other sentences that may exist. If we do not know what is or is not true then in any case...

    If the second sentence is referring to the first sentence:
    If it is true that the first sentence is false then the second sentence is true in stating that the first sentence is false. (= True)

    If it is true that the first sentence is true then the second sentence is false in stating that the first sentence is false. (= False)

    If the second sentence is referring to itself:
    If the sentence is true that it is false then the sentence is true that it is false. (= True)

    If the sentence is false that it is false then the sentence is false that it is false. (= False)
  • A few quick questions.
    I have multiple questions that need answering. — an-salad

    Ask multiple questions and you shall receive multiple answers.

    First, if there are infinite whole numbers, and there are infinite decimals between 0 and 1, and there are infinite decimals between 0.1 and 0.12, does that mean that infinity itself is infinitely infinite infinitely (etc.) ? — an-salad

    Definitely.

    Also, will there be a manned mission to m87 by 2030? — an-salad

    Tickets are on sale now!

    What if u brought a talisman from Cambodia? — an-salad

    Then it would not be in Cambodia anymore.

    Also, Ive never left Chicago in my life. How is it different out there? — an-salad

    I've never left Chicago either, nor have i gone there. The biggest difference is that i am not in Chicago.

    Is the sky purple? — an-salad

    I'm assuming the sky is purple in Chicago. The sky here where i live is iridescent, and it's located up and slightly to the left, but i'm not worried.

    Are there dinosaurs? — an-salad

    Many in fact, they come here for retirement.

    Are there three large moons? — an-salad

    Not always.

    Thnx for your answers in advance. :3 — an-salad

    You're welcome, and now they're your answers too. :-)
  • To what jazz, classical, or folk music are you listening?
    Nisi Dominus - Vivaldi - Collegium 1704



  • What Are You Watching Right Now?
    I Just finished watching this, and thought it was sufficiently thought-provoking to post here.

  • What are you listening to right now?
    bonus track:
  • What are you listening to right now?
    agr? — Changeling

    6 out of 10



  • What are you listening to right now?
    ↪Changeling


    I do indeed :up:

    Currently listening to:
  • What are you listening to right now?




    DIE ANTWOORD - FAT FADED FUCK FACE
  • What are you listening to right now?
    Merry Christmas music, and a happy new year!



    Psalm 58 (KJV)
    1 Do ye indeed speak righteousness, O congregation? do ye judge uprightly, O ye sons of men?
    2 Yea, in heart ye work wickedness; ye weigh the violence of your hands in the earth.
    3 The wicked are estranged from the womb: they go astray as soon as they be born, speaking lies.
    4 Their poison is like the poison of a serpent: they are like the deaf adder that stoppeth her ear;
    5 Which will not hearken to the voice of charmers, charming never so wisely.
    6 Break their teeth, O God, in their mouth: break out the great teeth of the young lions, O Lord.
    7 Let them melt away as waters which run continually: when he bendeth his bow to shoot his arrows, let them be as cut in pieces.
    8 As a snail which melteth, let every one of them pass away: like the untimely birth of a woman, that they may not see the sun.

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