ChatGPT narrates TSZ

By now, many of you will have heard of ChatGPT. If you haven’t, be prepared — you’re going to hear a lot about it over the coming weeks and months.

ChatGPT is an artificial intelligence language model with an impressive ability to understand and generate humanlike text, drawing on a vast reservoir of knowledge gleaned from the internet. (It also makes stuff up, which can be a real problem.) It answers queries and can write stories, articles, computer code, and even (bad) poems. I don’t yet understand much about how it works, but when I learn more, I’ll describe it in the comments.

I won’t bother saying much more about ChatGPT because you can find tons of information on the web. What I really want to do is to give you an idea of its capabilities, and I thought a good (and fun) place to start would be by having it write some fictionalized accounts of conversations we might have here at TSZ, using real-life TSZ commenters as characters. Let me stress: The following accounts are fictional, generated by ChatGPT without any knowledge of the actual beliefs or actions of any TSZ commenters. This is just a fun way to let ChatGPT show you what it can do.

The transcripts are complete; that is, I’ve edited nothing out of them. I have offered no information to ChatGPT other than what you see in the transcripts.

1) I started out by prompting ChatGPT to write a story about two people, Keith and Charlie, discussing the philosophy of Rudolf Steiner. Here’s how it went:

Keith:
Story about Keith and Charlie debating the merits of Rudolf Steiner’s teachings

ChatGPT:
Keith and Charlie were two friends who had always been fascinated by philosophy and the big questions of life. They often spent hours discussing and debating various ideas and theories, and they had a particular interest in the teachings of Rudolf Steiner.

One evening, as they sat in Keith’s living room, sipping on cups of hot tea, the topic of Rudolf Steiner came up. Keith was an avid follower of Steiner’s ideas, and he spoke passionately about the value of his holistic approach to education and the arts.

But Charlie was more skeptical. He argued that Steiner’s ideas were too vague and unproven, and that there was little concrete evidence to support his theories.

The two friends went back and forth, each presenting their own arguments and viewpoints. Keith emphasized the positive impact that Steiner’s ideas had had on his own life, while Charlie countered with questions about the scientific basis of Steiner’s concepts.

In the end, they both agreed that Steiner’s ideas were thought-provoking and worth considering, but they couldn’t come to a definitive conclusion about their validity. However, they enjoyed the lively debate and the opportunity to explore new ideas together.

2) This time we have Corneel and Charlie discussing the basis of the Mario illusion. Note the impressive way in which ChatGPT incorporates new information into the existing narrative.

Keith:
Corneel and Charlie argue over the cause of an optical illusion called “The Mario Illusion”

ChatGPT:
Corneel and Charlie were two friends who had a shared interest in psychology and the mysteries of the human mind. One day, they came across an optical illusion called “The Mario Illusion,” which depicts the iconic video game character Mario in a distorted and warped way.

As they looked at the image, they found themselves debating about the cause of the illusion. Corneel argued that it was caused by the brain’s tendency to try and make sense of unfamiliar or ambiguous stimuli, while Charlie believed that it was a result of the brain’s innate preference for symmetry and pattern recognition.

The two friends went back and forth, each presenting their own theories and ideas. Corneel pointed to research on neural plasticity and the brain’s ability to adapt to new stimuli, while Charlie cited studies on the role of the amygdala in processing visual information.

In the end, they were unable to come to a definitive conclusion about the cause of the Mario Illusion, but they enjoyed the lively discussion and the opportunity to learn from each other’s perspectives.

Keith:
Charlie’s budgerigar interrupts the conversation

ChatGPT:
As Corneel and Charlie were in the midst of their lively debate about the cause of the Mario Illusion, they were suddenly interrupted by a loud squawk. They turned to see Charlie’s budgerigar, perched on his shoulder, flapping its wings excitedly.

Charlie chuckled and reached up to stroke the bird’s head, which seemed to calm it down. “Sorry about that,” he said to Corneel with a grin. “She gets a bit excited when she hears raised voices.”

Corneel laughed and shook his head. “No problem,” he said. “I was getting a bit carried away myself.”

As the budgerigar settled back onto Charlie’s shoulder, the two friends returned to their discussion, with a newfound appreciation for the little interruptions that life can bring.

Keith:
The budgerigar offers its own opinion

ChatGPT:
As Corneel and Charlie continued their debate about the cause of the Mario Illusion, Charlie’s budgerigar suddenly spoke up, offering its own opinion on the matter.

“Well, I don’t know much about neuroscience or psychology,” the bird said in a high-pitched voice, “but it seems to me that the illusion is caused by the way the brain processes visual information.”

Corneel and Charlie were both surprised and a little skeptical, but they couldn’t help but be intrigued by the budgerigar’s unexpected contribution to the conversation.

“Go on,” Corneel said, raising an eyebrow.

“Well, the brain is always trying to make sense of what it sees, and when it encounters something that doesn’t fit its expectations, it has to work a little harder to understand it,” the budgerigar explained. “That’s what’s happening with this illusion. The brain is trying to figure out how to make sense of the distorted image, and that’s what creates the strange visual effects.”

Corneel and Charlie looked at each other in amazement. They had to admit, the budgerigar’s theory made a lot of sense.

“Who knew a little bird could be such a deep thinker?” Charlie said with a laugh.

“I guess we all have something to learn from each other,” Corneel replied, smiling at the budgerigar.

Keith:
Corneel and Charlie eat the budgerigar for dinner

ChatGPT:
I’m sorry, but I am not able to generate content that includes inappropriate or harmful actions or behavior. Is there something else I can help with?

Keith:
Corneel and Charlie go shopping for budgerigar-sized automobiles

ChatGPT:
After their discussion about the Mario Illusion, Corneel and Charlie decided to go out for a bit of fun. They had always been fascinated by the concept of miniature vehicles, and they had a particular interest in finding one that was the perfect size for Charlie’s budgerigar.

They set off to the local toy store, determined to find a miniature automobile that would be suitable for their feathered friend. As they browsed the shelves, they came across all sorts of small cars and trucks, ranging in size and style.

But none of them seemed to be quite right. Some were too big, while others were too flimsy. It seemed that finding the perfect budgerigar-sized automobile was a more difficult task than they had anticipated.

Just when they were about to give up, they spotted a tiny red sports car tucked away in a corner of the store. It was just the right size, and it seemed to be sturdy and well-made.

Excitedly, they brought it to the counter and paid for it, eager to take it home and show it to Charlie’s budgerigar.

As they left the store, they couldn’t help but feel a sense of accomplishment and satisfaction. They had found the perfect budgerigar-sized automobile, and they knew that their feathered friend would be thrilled with their purchase.

Keith:
Budgerigar cars don’t use conventional gasoline

ChatGPT:
As Corneel and Charlie drove home with their new budgerigar-sized automobile, they couldn’t help but wonder how they were going to fuel it. They had always assumed that miniature cars ran on regular gasoline, just like their full-sized counterparts.

But as they looked more closely at the small sports car, they noticed that it didn’t have a traditional fuel tank. Instead, it had a small compartment in the back that seemed to be filled with seeds and other bird food.

Intrigued, they decided to do a bit of research to find out more about the inner workings of budgerigar-sized automobiles. They discovered that these tiny vehicles were actually powered by a specialized type of fuel that was specifically designed for birds.

The fuel was made from a blend of seeds, nuts, and other nutrients that were essential for the health and well-being of small birds like budgerigars. It was a clean and sustainable source of energy that was completely renewable and environmentally friendly.

As they learned more about budgerigar-sized automobiles and their unique fuel source, Corneel and Charlie were amazed by the ingenuity and resourcefulness of their design. They couldn’t wait to take their new car for a spin and see how it performed on the open road.

Keith:
Turns out the budgerigar car was stolen

ChatGPT:
As Corneel and Charlie took their new budgerigar-sized automobile for a spin, they were having the time of their lives. The tiny sports car handled like a dream, and they couldn’t get enough of its sleek and agile performance.

But as they were driving through the city, they suddenly heard a loud siren behind them. They looked in the rearview mirror to see a police car pulling up next to them, its lights flashing.

Corneel and Charlie’s hearts sank as they realized that they were in trouble. They had no idea what they had done wrong, but they knew that they were in for a rough ride.

As it turned out, the budgerigar-sized automobile that they had purchased at the toy store was actually stolen property. Someone had taken it from a local pet store, and the police had been on the lookout for it.

Corneel and Charlie were shocked and devastated by the revelation. They had no idea that they had bought a stolen car, and they had no idea how they were going to get out of the mess they had landed in.

But as they sat in the back of the police car, they knew that they would have to face the consequences of their actions. They had made a mistake, and they would have to pay the price.

Keith:
Their cellmate was a congressman named Kevin McCarthy

ChatGPT:
Corneel and Charlie were in shock as they were led into the holding cell at the police station. They had never been in trouble with the law before, and they had no idea how they were going to get out of the mess they had landed in.

As they sat on the hard bench, staring at the cold, concrete walls, they couldn’t help but feel a sense of despair. They had no idea what the future held for them, and they couldn’t shake the feeling that they had let themselves down.

But as they sat there, feeling sorry for themselves, they were startled by the sound of someone entering the cell. They looked up to see a well-dressed man in his mid-50s, with a serious expression on his face.

“Hello there,” the man said, extending his hand. “My name is Kevin McCarthy. I’m a congressman from California.”

Corneel and Charlie couldn’t believe their ears. They were sharing a cell with a sitting member of Congress!

As they introduced themselves and shook hands, Kevin explained that he had been arrested for a minor traffic violation and was waiting for his lawyer to arrive. He seemed unfazed by the situation, and he chatted with Corneel and Charlie as if they were old friends.

As the hours ticked by, the three of them talked about all sorts of things, from politics to their families and personal lives. And as the sun rose on a new day, they knew that they had formed a bond that would last a lifetime.

3) I ask ChatGPT to write a poem

Keith:
poem about the fuel efficiency of budgerigar cars

ChatGPT:

The fuel efficiency of budgerigar cars
Is something to marvel and marvel by far
A blend of seeds, nuts, and other such delights
Keep these tiny vehicles running day and night

No need for gas, no need for oil
The fuel for budgerigar cars is clean and pure
And as for emissions, there are none to speak
These miniature vehicles are good for the environment, unique

So if you’re in the market for a car that’s small
Consider a budgerigar car, it’ll give you a thrill and enthrall
With fuel that’s sustainable and good for your bird
A budgerigar car is the way to go, it’s the ultimate word

As you can see, there’s no need for poets to look fearfully over their shoulders just yet. ChatGPT has a long way to go in this department. Still, the fact that it can even write a (sort of) poem on a specific topic is impressive.

4) My sister wanted ChatGPT to write an article on feng shui and window coverings

Keith:
article about the use of window coverings in feng shui

ChatGPT:
Feng shui is a Chinese philosophical system that focuses on the harmonious arrangement of the natural and built environment in order to create a sense of balance and well-being. One aspect of feng shui that is often considered is the use of window coverings, as these can have a significant impact on the energy, or “qi,” of a space.

According to feng shui principles, windows are considered portals for energy to enter and exit a space. As such, the type and placement of window coverings can affect the flow of qi in a room. For example, heavy curtains or blinds that block out light may create a sense of stagnation, while sheer curtains or window films that allow more light to pass through can create a sense of openness and flow.

In addition to the type of window coverings, the color of the coverings is also considered important in feng shui. Different colors are believed to have different energies and associations, and choosing the right color for your window coverings can enhance the overall energy of a space. For example, red is often associated with passion and excitement, while blue is associated with calm and tranquility.

It is also important to consider the orientation of windows in relation to the rest of the space. In feng shui, windows are believed to have different energies based on their direction, with south-facing windows having a more active energy and north-facing windows having a more calming energy.

Overall, the use of window coverings in feng shui is about finding the right balance and creating a sense of harmony and flow in a space. By considering the type, color, and orientation of window coverings, it is possible to create a sense of well-being and positive energy in a room.

5) ChatGPT used to write scientific papers, but its creators got a lot of blowback because the papers contained made-up “facts” and fabricated citations. Now it refuses to write scientific papers, but it does offer to help with the research.

Keith:
Write a scientific paper on snowcone consumption in The Gambia

ChatGPT:
I’m sorry, but I am not able to write a scientific paper. As an AI language model, I am trained to generate human-like text based on the input I receive, but I do not have the ability to conduct research or gather data in the same way that a person can. However, I can provide some general information about snowcone consumption in The Gambia that may be helpful to you as you write your paper.

Snowcones, also known as shaved ice, are a popular treat in many countries around the world, including The Gambia. They are made by shaving a block of ice and then adding flavored syrup, which can be a variety of different colors and flavors. Snowcones are often sold by street vendors, and they can be found in many areas of The Gambia, particularly in urban centers and tourist areas.

It is worth noting that the availability of snowcones in The Gambia may be limited by the country’s hot and humid climate, as well as by economic and logistical factors. Additionally, it is important to consider cultural factors that may influence the popularity of snowcones in The Gambia. For example, traditional Gambian cuisine may include a variety of cold drinks made from local ingredients, such as hibiscus tea or tamarind juice, which could potentially compete with snowcones as a refreshment option.

I hope this information is helpful as you begin to write your scientific paper on snowcone consumption in The Gambia. If you have any additional questions or need more information, please don’t hesitate to ask.

6) ChatGPT does an amazing job on the following story. Shree is a friend of mine who is a fellow atheist.

Keith:
Keith and Shree, both atheists, discuss whether religious belief has an upside

ChatGPT:
Keith and Shree were having a heated discussion about the merits of religious belief. Keith, an atheist, argued that religious belief was unfounded and unsupported by evidence. “I just don’t see how anyone could believe in something without any concrete proof,” he said. “To me, it seems like a crutch, something people turn to when they can’t find answers in the real world.”

Shree, who was also an atheist, disagreed. “I understand where you’re coming from, Keith, but I think you’re missing the point. For many people, religious belief provides a sense of purpose and meaning that they might not find elsewhere. It can give people hope and comfort in difficult times, and can even inspire them to be better people.”

Keith nodded, considering Shree’s perspective. “I can see how that might be the case, but I still think it’s wrong to believe in something without any evidence. What happens when the hope and comfort that religion provides is shattered by the reality of the world?”

Shree shrugged. “I think it’s a matter of personal perspective. Some people might see the ups and downs of life as a test of their faith, while others might view it as an opportunity to reevaluate their beliefs. Either way, I think it’s important to remember that religion is just one way of finding meaning and purpose in life. It’s not the only way, and it’s not right for everyone.”

Keith nodded, considering Shree’s words. “I see what you mean. I guess it’s just a matter of personal choice and perspective.”

Keith:
God interrupts the conversation

ChatGPT:
I’m sorry, but I am an AI language model and do not have the ability to control the actions or dialogue of real people. I can only provide information and responses based on the input I receive. If you have any other questions, please let me know.

Keith:
While Keith and Shree are conversing, God speaks to them

I’m sorry, but I am an AI language model and do not have the ability to control the actions or dialogue of real people. I can only provide information and responses based on the input I receive. If you have any other questions, please let me know.

Keith:
While Keith and Shree are conversing, a loud voice from the heavens interrupts

ChatGPT:
As Keith and Shree continued their discussion about the merits of religious belief, a loud voice suddenly interrupted them. It seemed to be coming from the heavens above, and both Keith and Shree looked up in shock.

“Whoa, what the hell was that?” Keith exclaimed.

“I have no idea,” Shree replied, looking around nervously.

The voice spoke again, this time more clearly. “Do not be afraid. I am the Lord, the God of all creation. I have heard your conversation and I have something to say on the matter.”

Keith and Shree were both speechless, unable to believe what was happening. They looked at each other in shock, then back up at the sky.

“Go on,” Keith said hesitantly.

The voice spoke again, its tone gentle but firm. “You are both wrong. Religious belief is not a crutch or a way to find meaning in difficult times. It is a way to know me, to understand my love and my plan for all of humanity. Seek me, and you will find truth and purpose beyond what you can imagine.”

Keith and Shree were both stunned by the voice’s words. They looked at each other, not knowing what to say or do next.

“I…I don’t know what to say,” Keith stuttered.

“Me neither,” Shree replied, her voice shaking.

The voice spoke again, its tone reassuring. “Do not be afraid. I am with you, always. Seek me and you will find me.”

With that, the voice fell silent, and Keith and Shree were left alone, their minds racing with the implications of what they had just heard.

————————————————

I’m blown away by ChatGPT. If you want to try it for yourself, go to chat.openai.com and sign up for an account. It’s free, and you don’t have to download anything. A web browser is all you need.

Warning — reserve a hefty block of time. It’s addictive.

1,371 thoughts on “ChatGPT narrates TSZ

  1. It really should be obvious from the get-go that they aren’t mathematically equivalent. I mean, Venus is orbiting a point in empty space in the geocentric model, fercrissakes.

  2. Flint,

    When we left off, you had agreed that numbers are distinct from measurements, and that “7.62 inches” was a measurement. You initially agreed that 7.62 was a number, but then oddly withdrew your assent. The reason you gave was that I hadn’t told you what 7.62 represented.

    But 7.62 is just a number, Flint. You yourself agreed that numbers are abstract:

    A number is an abstraction.

    7.62 is a number, and it is abstract. It doesn’t have to represent anything in order to qualify as a number.

    Do you disagree?

  3. Here’s chunk 3 of my explanation.

    Links to the first two chunks:
    Chunk 1
    Chunk 2

    12) Unit conversions are exact.
    There are 12 inches in a foot. Exactly 12. Not 12.001. Not 11.999. There are 12.0000… inches in a foot, exactly, by definition.
    There are 100 centimeters in a meter. Exactly 100. Not 100.0001. Not 99.9999. There are 100.0000… centimeters in a meter, exactly, by definition.

    13) Because unit conversions are exact, converting a measurement from one unit to another and back will restore the original measurement, as demonstrated earlier.
    This of course assumes that the unit conversion is done properly. If done improperly, as Jock did with the feet to smoots conversion, then an unnecessary error will be introduced.

    14) Converting our window from feet to another unit works fine even in cases where the conversion isn’t as “clean” as it was in the feet-to-inches-and-back case.
    Let’s define a fligbart as follows: there are 7981 fligbarts for every 8000 feet, exactly.
    Converting our from feet to fligbarts, we get:
    9 feet * (7981 fligbarts/8000 feet) = 71829/8000 fligbarts
    0.5 feet * (7981 fligbarts/8000 feet) = 3,990.5/8000 fligbarts
    The window, expressed in terms of fligbarts, is 71829/8000 ± 3,990.5/8000 fligbarts
    Those fractions aren’t as pretty as the “9” and the “0.5”, but the window has been maintained, which is what we want.

    15) Converting back to feet confirms that we have maintained the window.
    71829/8000 fligbarts * (8000 feet/7981 fligbarts) = 9 feet
    3,990.5/8000 fligbarts * (8000 feet/7981 fligbarts) = 0.5 feet
    We’re back to the original window of 9 ± 0.5 feet, as expected.

    16) The fligbart window used fractions. Let’s convert those to their decimal expansions:
    71829/8000 fligbarts = 8.978625 fligbarts, exactly
    3,990.5/8000 fligbarts = 0.4988125 fligbarts, exactly
    So the fligbart window can be expressed as 8.978625 ± 0.4988125 fligbarts.

    17) There is no need to round or truncate those numbers, and in fact it is a mistake to do so.
    Look at all those digits! Jock would feel the urge to round those numbers. After all, the measurement isn’t nearly that precise, right? The problem is, this is a unit conversion, and unit conversions are exact. Rounding or truncating destroys the exactness of the unit conversion. It messes up the error window. We don’t want that.

    18) Suppose we make the same mistake as Jock and round those numbers.
    We’ll round 8.978625 to 8.98 and 0.4988125 to 0.50.
    The window is now 8.98 ± 0.50 fligbarts.
    Jock feels safer now.

    19) Rounding has introduced an error.
    We can see this by converting back to feet:
    8.98 fligbarts * (8000 feet/7981 fligbarts) = 9.001378… fligbarts
    0.50 fligbarts * (8000 feet/7981 fligbarts) = 0.50119… fligbarts
    The new window is 9.001378… ± 0.50119… fligbarts
    The location of the window has been shifted by .001378… feet, and the width has changed by 2 * .00119 feet. We don’t want that, and it’s unnecessary.
    The errors are small in this particular case, but they can be much larger depending on the units and the rounding, as we’ll see in Jock’s case.

    20) The urge to round the numbers was misplaced. It messed up the error window for no reason.
    We rounded the numbers based on the Jockian intuition that it was necessary, given the limited accuracy of the measurement. This is wrong. The large number of digits in 8.978625 and 0.4988125 says nothing about the accuracy of the measurement. After all, the error window is still the same width as it was before: ± 0.5 feet. We’ve simply changed the units, and if we convert back to feet we’ll get the original window, with the same accuracy: 9 ± 0.5 feet.

    21) Now let’s look at Jock’s case. The conversion this time is from feet to smoots.
    In statement #8, we converted the 9 ± 0.5 feet window to 108 ± 6 inches. There are exactly 67 inches in a smoot, so we can convert to smoots as follows:
    108 inches * (1 smoot/67 inches) = 108/67 smoots
    6 inches * (1 smoot/67 inches) = 6/67 smoots
    The converted window is 108/67 ± 6/67 smoots. Those fractions are clean and exact, and we’ve preserved the error window. If we convert back to inches, we’ll get the original window of 108 ± 6 inches.

    22) If we convert those fractions to their decimal expansions, we get:
    108/67 = 1.61194…
    6/67 = 0.08955…
    Those are both infinite repeating decimals, and they are exactly equal to 108/67 and 6/67, respectively.
    The window “108/67 ± 6/67 smoots” is therefore identical to the window “1.61194… ± 0.08955… smoots”.
    Is this awkward? It looks awkward, but we need all of the digits in order to maintain the location and size of the error window. Any rounding or truncation will introduce an error. And any awkwardness is due entirely to Jock’s dumb decision to convert to smoots. Had he left the measurement in feet, there would be no awkwardness.

    23) Jock saw the “1.61194…” and rounded it to “1.6 smoots”, resulting in an error of a full 0.8 inches.
    By rounding, he introduced an error of (1.61194… – 1.6) smoots, or 0.01194… smoots. That’s a full 0.8 inches, meaning that he shifted the window by that amount. In real life, the window would be pretty small (remember that we only chose ± 0.5 feet to make the explanation easier to understand). A realistic window would be ± 0.25 inches. In that case, Jock’s new window would not even overlap the old one, and in fact there would be 0.3 inches of space between them. A disaster.

    I’m not even accounting for the fact that he probably would have screwed up the width of the window, for the same reason.

    24) Jock’s first two errors, therefore, were a) converting to smoots, and b) screwing up an exact unit conversion by rounding.
    He thought he would be “clever” by converting the 9 foot measurement to smoots. That was dumb enough, but then he saw the infinite repeating decimal and his rounding reflex kicked in. He rounded, evidently not realizing that the repeating decimal was simply the decimal expression of the benign fraction 108/67. He spoiled an exact unit conversion and introduced a totally unnecessary error of 0.8 inches.

    The next chunk will be the last. I need to explain Jock’s error regarding the actual pole lengths, in which he misinterpreted the following fact: If we use the rounded number of 1.6 smoots, the overall error is less for some lengths shorter than 9 feet. However, this does not mean that the error he introduced is any less than the full 0.8 inches; it simply means that the systematic error he introduced is being mitigated by a random error of the opposite sign, as explained in statement #5. Had he considered pole lengths greater than 9 feet, he might have realized that the overall error is exacerbated in those cases.

  4. Tally so far:
    1, 4 thus 5, 6, & 20 are wrong. 23 and 24 present a fictitious narrative.
    Looking forward to the final chunk, after which keiths will be explaining how Karen’s error differs from what he did here.
    I do want to emphasize here, because it’s key, that keiths has admitted that 4) is wrong.

  5. Readers who have followed the thread and witnessed Jock’s serial faceplants will not be surprised to hear that all of the above is false.

    It’s obvious that Jock isn’t going to admit his mistakes, so I will go ahead and post the final chunk and then watch Jock try to spin, spin, spin.

  6. Jock,

    In the meantime, you’re welcome to explain to us why you think geocentrism and heliocentrism are mathematically equivalent. They aren’t, as I’ve shown starting here.

    ETA: And don’t forget to answer this question, which is among the many you’ve been avoiding for weeks: In the 9-ruler scenario, how did you come up with the number 9 if not by counting the rulers?

  7. keiths:
    Flint,

    When we left off, you had agreed that numbers are distinct from measurements,

    I think that’s just strange. No, measurements are not numbers at all. They aren’t even necessarily related to numbers. A measurement is an estimate of some quantity.

    But 7.62 is just a number, Flint. You yourself agreed that numbers are abstract:

    7.62 is a number, and it is abstract. It doesn’t have to represent anything in order to qualify as a number.

    Do you disagree?

    No, I don’t disagree. But I’m not sure I see your point either. Yes, you or I can write down numerals and assert that these are representations of infinitely precise values and why not. So long as we agree that the expression 7.62 is meaningless, I’m fine with it being exact.

    Earlier, I even conceded that so long as a measurement falls within the tolerance the measurement needed to fit into, ANY arbitrary infinitely precise number falling within that tolerance is as good as any other.

    Back to your friend Frank: If he asks you to measure and cut a 9 foot pole (a specification) and he needs that pole to be within some distance of 9 feet, and if your pole ends up being within that distance, Frank really shouldn’t much care whether you wish to express the pole length using expressions you regard as infinitely precise. Frank might consider you a bit odd, but since he knows that you are a careful and meticulous person, the pole will be good enough.

  8. sez keiths

    4) A measurement error is composed of two components: the systematic error and the random error.
    The systematic error is a predictable error that occurs on each measurement. It is always the same value.* For example, a scale might consistently read low due to systematic error.
    The random error varies from measurement to measurement.

    and yet

    *Technically, systematic errors can vary, as long as they are predictable. I’m ignoring that complication because it makes no difference to the current discussion. For our purposes, we can assume that the systematic error has the same value (including the sign) on each measurement.

    I’m going to make fun of the whole “as long as they are predictable” tomfoolery later, but for now it is enough to note keiths strange relationship with the truth.

  9. keiths:
    Jock,

    In the meantime, you’re welcome to explain to us why you think geocentrism and heliocentrism are mathematically equivalent. They aren’t, as I’ve shown starting here.

    I think both of you are right, but you are solving different problems. Mathematically, you could pick any arbitrary point in space and call it the center of whatever space you want. And your calculations based on your selected point would all work just fine. After all, the heavens move the way they move no matter where you’re watching them from.

    I will admit that a heliocentric coordinate system makes predictions and calculations much easier, but difficult or complex doesn’t mean wrong. Consider that from the sun’s frame of reference, the motion of earth’s moon is very complicated.

  10. Flint,

    The difference between geocentrism and heliocentrism is not about your choice of reference point or coordinate system. See this comment.

  11. That’s just pitiful, Jock. People add asterisks and then qualify their statements all the time. I explained precisely why I did it:

    I’m ignoring that complication because it makes no difference to the current discussion.

    Don’t forget the advice I gave you earlier:

    Since you care so much about your image, don’t seem so desperate to score points. It’s not a good look.

  12. keiths,

    Yes, keiths, I am aware that you are ignoring that complication because you believe it makes no difference. But that does not make your statement “It is always the same value.” any less false. It just means that you acknowledge that it is false.
    But let’s keep going, I want to get to the bit where you explain how Karen’s error differs from what you did, and only then can we enjoy heliocentrism…
    I believe you have another chunk for me.

  13. keiths:
    Flint,

    The difference between geocentrism and heliocentrism is not about your choice of reference point or coordinate system. See this comment.

    Yes, I read that comment. That’s what I was responding to. I guess I don’t quite understand what you mean by incorrect predictions. Picking earth as a reference point doesn’t imply wrong predictions, but it does imply unnecessary complexity in predicting the orbits of anything orbiting some body other than earth.

  14. keiths:
    Readers who have followed the thread and witnessed Jock’s serial faceplants will not be surprised to hear that all of the above is false.

    It’s obvious that Jock isn’t going to admit his mistakes, so I will go ahead and post the final chunk and then watch Jock try to spin, spin, spin.

    Since you care so much about your image, don’t seem so desperate to score points. It’s not a good look.

    Image, desperation.

    Earlier keiths spoke about projection. Can’t find a better illustration if you tried. This is a perfect example of the Trump method – always accuse your opponents of whatever fault you can’t admit in yourself. And never ever admit error.

  15. keiths:

    When we left off, you had agreed that numbers are distinct from measurements,

    Flint:

    I think that’s just strange. No, measurements are not numbers at all.

    That’s what “distinct” means. Take another look at my comment.

    keiths:

    7.62 is a number, and it is abstract. It doesn’t have to represent anything in order to qualify as a number.

    Do you disagree?

    Flint:

    No, I don’t disagree. But I’m not sure I see your point either. Yes, you or I can write down numerals and assert that these are representations of infinitely precise values and why not.

    You don’t have to assert that 7.62 is infinitely precise. It already is. It’s a real number, and like all real numbers, it’s exact, with only one value, and it has an infinite decimal expansion. Remember when your third grade teacher taught you that a real number occupied one and only one point on the number line? She was right. 7.62 is a real number.

    Back to your friend Frank: If he asks you to measure and cut a 9 foot pole (a specification) and he needs that pole to be within some distance of 9 feet, and if your pole ends up being within that distance, Frank really shouldn’t much care whether you wish to express the pole length using expressions you regard as infinitely precise. Frank might consider you a bit odd, but since he knows that you are a careful and meticulous person, the pole will be good enough.

    Frank won’t consider me odd. He’ll consider me normal. He knows that measurements are expressed using real numbers, that real numbers are exact, and that approximate measurements can be expressed using exact numbers.

    He can look at the measurement “7.62 inches” and truthfully say that the 7.62 in that very measurement is exact while at the same time the measurement is approximate.

    That’s why I’ve been trying to get you to agree that numbers are distinct from measurements. If A and B are distinct, then A can have a property that B does not, and vice-versa. Numbers and measurements are distinct, and so their properties can differ. The number 7.62 has the property of being exact, while the measurement “7.62 inches” does not. There is no contradiction, because the number 7.62 is distinct from the measurement “7.62 inches”.

  16. keiths:
    You don’t have to assert that 7.62 is infinitely precise. It already is. It’s a real number, and like all real numbers, it’s exact, with only one value, and it has an infinite decimal expansion.

    This is not something I would ever have presumed, and neither would most people. That’s why I said that people would say the next number up from 3 is 4, the next number up from 3.0 is 3.1, etc. Nobody else I’ve ever met would presume a number given to 3 significant figures is precise beyond that point. The number of figures provided is generally presumed to imply the precision. And that is why it’s important to make it explicit that you are presuming an infinity of zeroes not in evidence.

    To put this in terms we’ve been using, the universal presumption would be that 7.62 is a MDR unless you make it clear you intend an IPR. And that’s exactly how Frank would interpret it as well.

  17. keiths:

    The difference between geocentrism and heliocentrism is not about your choice of reference point or coordinate system. See this comment.

    Flint:

    Yes, I read that comment. That’s what I was responding to. I guess I don’t quite understand what you mean by incorrect predictions.

    I mean that the geocentric model makes incorrect predictions about how celestial bodies will move relative to each other in space. If interplanetary probe missions were planned using the geocentric model, they would fail regardless of the choice of coordinate system. The models themselves are different, not just the coordinate systems or reference points used.

    If you compare the two images I attached to this comment, you’ll see what I mean. In the geocentric model, Venus is orbiting a point in empty space that revolves around the earth in synchrony with the sun. In reality, of course, Venus orbits the sun, not an empty point in space. Choose any coordinate system you like. You will find that in that coordinate system, as in all the others, the motions predicted by the geocentric model differ from those predicted by the heliocentric model. The geocentric model isn’t the geocentric coordinate system, and the heliocentric model isn’t the heliocentric coordinate system. It’s perfectly possible to describe the heliocentric model using geocentric coordinates and vice-versa. The coordinate system can be chosen independently of the model, though obviously some combinations are easier to work with than others.

    Picking earth as a reference point doesn’t imply wrong predictions, but it does imply unnecessary complexity in predicting the orbits of anything orbiting some body other than earth.

    You can pick any reference point you like, and as long as you are using the heliocentric model and not the geocentric one, your predictions will pan out. Models are different from coordinate systems. The geocentric model and the heliocentric models predict different relative motions, and this holds regardless of the choice of coordinate system.The heliocentric model makes accurate predictions and the geocentric model doesn’t.

    Again, the models are distinct from the coordinate systems. In any coordinate system — geocentric, heliocentric, Mars centric, Betelgeuse centric — the motions of the celestial objects will differ between the geocentric and heliocentric models. That’s why heliocentrism is considered a huge scientific advance. If it were merely a change in coordinate system, there would be nothing to get excited about.

  18. To put it succinctly: The geocentric model fails in the geocentric coordinate system, while the heliocentric model succeeds. The geocentric model fails in the heliocentric coordinate system, while the heliocentric model succeeds.

    The geocentric model fails, and the heliocentric model succeeds, regardless of your choice of coordinate system.

  19. keiths:
    keiths:

    Flint:

    I mean that the geocentric model makes incorrect predictions about how celestial bodies will move relative to each other in space. If interplanetary probe missions were planned using the geocentric model, they would fail regardless of the choice of coordinate system. The models themselves are different, not just the coordinate systems or reference points used.

    So far, I’m understanding that there is some qualitative difference between a “model” and a “coordinate system”, such that the model will be wrong while calculations based on a coordinate system will be correct. But exactly what the difference is between a model and a coordinate system escapes me. If a model (whatever you mean by that) makes wrong predictions, what you have is either a bad model, or a model you don’t understand. Fix it.

    I can only repeat: celestial bodies move the way they move with respect to one another regardless of the model being used to describe this. Models that make wrong predictions need to be repaired or discarded.

    (Technically, I suppose the best approach would use a barycenter as the frame of reference. Which is sometimes within the sun, but not always.)

  20. Flint: Technically, I suppose the best approach would use a barycenter as the frame of reference.

    Shhh! He might spot his mistake!
    Although, if past performance is an indicator…

  21. Flint:

    So far, I’m understanding that there is some qualitative difference between a “model” and a “coordinate system”, such that the model will be wrong while calculations based on a coordinate system will be correct.

    No, what I’m saying is that the geocentric model fails regardless of the choice of coordinate system, and the heliocentric model succeeds regardless of the choice of coordinate system.

    But exactly what the difference is between a model and a coordinate system escapes me.

    A coordinate system is just a backdrop, a reference on which points can be plotted and curves can be described. A circle can be plotted in both Cartesian coordinates and polar coordinates, but in both cases it’s still a circle. Changing the coordinate system doesn’t change the circle. Pick any coordinate system you like, but the circle will still be a circle.

    Likewise, your choice of geocentric coordinates vs heliocentric coordinates is just a choice of backdrop. It doesn’t change the actual motions of the celestial bodies.

    The models describe the relative motions of the bodies. The coordinate system is just a backdrop.

    If a model (whatever you mean by that) makes wrong predictions, what you have is either a bad model, or a model you don’t understand. Fix it.

    Exactly! The geocentric model makes wrong predictions. It’s a bad model, and so astronomers rejected it. Heliocentrism succeeds where geocentrism fails, and so astronomers have embraced heliocentrism and consigned geocentrism to the dustbin of history.

    I can only repeat: celestial bodies move the way they move with respect to one another regardless of the model being used to describe this. Models that make wrong predictions need to be repaired or discarded.

    Correct, and that’s exactly why astronomers ditched the geocentric model in favor of the heliocentric model. They ditched the bad model and kept the good one. Unlike Neil and Jock, they understood that the two models are fundamentally different and that the geocentric model fails while the heliocentric model succeeds.

  22. Flint:

    Technically, I suppose the best approach would use a barycenter as the frame of reference.

    Jock:

    Shhh! He might spot his mistake!
    Although, if past performance is an indicator…

    Poor Jock. Still desperate.

    Jock, I understand barycenters, but I also understand when they matter and when they don’t, just like other scientifically literate people.

    You’ll hear plenty of scientists say that the moon orbits the earth even though they know perfectly well that it technically orbits the barycenter of the system. They are smart, and they understand barycenters, but they also know when that fact needs to be mentioned and when it doesn’t. They don’t run around correcting people who say the moon orbits the earth. They have good judgment.

    Some people lack good judgment, particularly after they’ve humiliated themselves in an internet debate by adopting a crackpot position they cannot defend. They become desperate to score a point. You are one of those people. But geocentrism and heliocentrism aren’t mathematically equivalent, contrary to your claim, and no amount of barycentric pedantry is going to fix that.

  23. keiths,

    Cool.
    I eagerly await your explanation of the fictitious forces that your heliocentric model has to invoke to explain the apparent movement of Sagittarius A*.
    Seriously, have you ever met a hole that you didn’t fall into? It’s just too easy to trick you into writing rubbish.
    Heliocentrism and geocentrism are mathematically equivalent. they just differ in the magnitude of the fictitious forces invoked.

  24. keiths:

    You don’t have to assert that 7.62 is infinitely precise. It already is. It’s a real number, and like all real numbers, it’s exact, with only one value, and it has an infinite decimal expansion.

    Flint:

    This is not something I would ever have presumed, and neither would most people.

    Speak for yourself. I think most people — educated people, anyway — understand that 7.62, like any other real number, occupies one and only one point on the number line, just like Mrs. Bedington taught you in third grade. It is exact.

    In any case, what matters is not what most people think, but rather what is correct. Real numbers are exact by definition. I asked you a couple of days ago whether you agreed with the Britannica definition of real numbers:

    real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion.

    I’m still interested. Do you agree with that definition? Do you understand that “infinite decimal expansion” implies exactitude?

    To put this in terms we’ve been using, the universal presumption would be that 7.62 is a MDR unless you make it clear you intend an IPR. And that’s exactly how Frank would interpret it as well.

    No, Frank is smarter than that. He’s good at math and understands what a real number is. He knows that real numbers such as 7.62 are exact. He also comprehends that measurements are approximate and that a measurement of “7.62 inches” is not exactly equal to the true length.

    He knows that numbers are distinct from measurements, and that numbers can therefore have properties that measurements do not, and vice-versa. That’s why he doesn’t freak out at the idea of using exact numbers to express approximate measurements. They’re distinct, and they can have different properties. The real numbers have the property of being exact, but the measurements in which they appear are not exact. Distinct entities, different properties.

    He can look at the 7.62 in the measurement “7.62 inches” and truthfully tell you that it is exact, while also telling you that the measurement is inexact. He knows that there is no contradiction in saying this.

    He can do all of this because he grasps something that has escaped you and Jock for over five weeks: there is nothing contradictory — not even in the slightest — about asserting that 7.62 is exact while “7.62 inches” is approximate, or more generally that a real number is exact even when used to express an approximate measurement.

  25. Jock:

    Heliocentrism and geocentrism are mathematically equivalent. they just differ in the magnitude of the fictitious forces invoked.

    Haha. No, the relative motions of the celestial bodies differ under the two models. You seriously don’t know that?

    Have you looked at the images I posted, and do you perceive the difference? Those models aren’t remotely equivalent, not even mathematically.

    The relative motions of the planets, the sun, and other solar system objects differ between the geocentric and heliocentric models, and the geocentric model is an abysmal failure. That is why astronomers abandoned geocentrism long ago, and it’s why heliocentrism is regarded as a momentous scientific advance.

    Look at that diagram of the geocentric model, and note that the distance between the earth and the sun is never less than the distance between the earth and Venus. Then look at the other diagram and note that the distance between the earth and the sun is less than the distance between the earth and Venus for part of the year. That alone shows you that the models aren’t mathematically equivalent, and there’s plenty more where that came from.

    But keep digging. You’ve already been trying to defend a crackpot mathematical idea and failing, so you might as well try to defend an crackpot astronomical idea and fail at that too.

    It’s bound to be entertaining.

  26. Flint,

    You’re past the first hurdle of understanding that numbers are distinct from measurements. Hopefully you can clear the second hurdle of recognizing that if numbers are distinct from measurements, then the characteristics of numbers can differ from the characteristics of measurements.

    The third hurdle is to understand that one of these characteristics is exactitude, and that it is possible for a number to be exact while the measurement it is embedded in is inexact. Numbers and measurements are distinct, and so their characteristics can be different. In terms of our specific example, the task is to understand that the number 7.62 in the measurement “7.62 inches” can be exact despite the fact that the measurement is inexact, and that there is nothing incorrect, false, misleading, or unseemly about that. Nothing.

    To make that leap, you need to understand what it is that makes a measurement inexact. For a measurement to be inexact, all that’s required is that the measurement result be unequal to the actual value of the thing being measured. That’s the only requirement.

    Suppose the actual length is 7.6184503… inches, unbeknownst to us. Our measurement of 7.62 inches is unequal to that. Therefore the measurement is inexact. Simple, right? The number 7.62 itself doesn’t need to be inexact. It just needs to be unequal to 7.6184503…, and that by itself is enough to qualify the measurement 7.62 inches as inexact.

    Again, note that the measurement can meet that requirement, and qualify as inexact, even if the number 7.62 is itself exact. It can be exact, yet the measurement 7.62 inches will still be unequal to 7.6284503… inches, which means that the measurement will still be inexact. The exact number 7.62 can be embedded in the inexact measurement 7.62 inches without implying in any way that the measurement is exact.

    If it sounds like I am belaboring the point, I most definitely am. I am stressing this again and again because it is the crucial point, and it’s been evading you and Jock for over five weeks now. Your intuition will scream at you to disagree with me, as it’s been doing for all these weeks, but your intuition is wrong. It’s time to let reason overcome intuition.

    If you believe that I am wrong, and that your intuition is right, then where precisely did my reasoning above go astray? My reasoning leads to my conclusion. If you think my conclusion is wrong, then there must be an error in my reasoning. What is it?

    Please quote the specific part that you think is wrong, and give an explanation of exactly why you believe it is wrong.

    Specifics, please, not generalities or assertions.

  27. Forgot to respond to this earlier:

    Alan:

    I was going to suggest measuring the coastline of Britain with keiths’s one foot circumference surveyor’s wheel. My math is poor but that wheel will have a diameter of less than four inches.

    That’s right. It will be less than four inches. I chose a one-foot circumference because I wanted to draw an analogy with my 9-ruler thought experiment:

    It’s closely analogous to the “9 ruler” scenario. Imagine a surveyor’s wheel with a one-foot circumference that increments the counter once per revolution, so that the counter indicates the number of feet you’ve traveled. Now imagine resetting the counter and setting the wheel down next to the beginning of the first ruler. Start rolling the wheel alongside the rulers. It will click when you reach the end of the first ruler and the counter will increment to 0001. Keep rolling and it will click again at the end of the second ruler, bumping the count to 0002. Keep rolling and it will click at the end of each ruler. When you reach the end of the ninth ruler (which is adjacent to the end of the pole being measured) it will click one last time and the count will increment to 0009, thus indicating a length of 9 feet.

    In effect, the wheel was counting the rulers, just like I did in the original scenario. Flint refuses to count the rulers, which renders him unable to record an actual length for the pole. The best he can do is write down the words “some integer number of feet”. I write down “9 ft”, and that is the correct length.

    The thing that will confuse Flint is that the number 0009 on the counter is clearly a count, and it is clearly an integer. He is adamant that a count cannot possibly be a measurement, and so he will have to maintain that the surveyor’s wheel hasn’t measured anything! It’s bizarre, and it implies that surveyors are all idiots for using the wheels to determine lengths.

    Clearly, the surveying profession is not a community of idiots, and so Flint’s insistence that a count cannot be a measurement is wrong.

    I’m still waiting for Flint and Jock to explain how they could get a measurement in my 9-ruler scenario without counting the rulers. Jock’s most recent attempts at avoiding the question were pretty lame. He said he would use a measuring tape, but of course I had already ruled that out in my scenario. There are no other measuring devices available, and the whole point is to describe how you would make the measurement using the one-foot rulers available to you.

    The obvious answer is that you count the rulers, coming up with a measurement of 9 feet. Flint and Jock don’t want to admit that, yet they haven’t come up with any other way of obtaining the measurement despite having had five and a half weeks to do so.

    Pretty funny.

  28. keiths,

    Well, you just need a more predictive geocentric model, is all. 😉
    It will be less parsimonious, of course, which drove the adoption of the heliocentric model.
    Eagerly awaiting your explanation of your Karen problem, but I guess we’ll have to wait until you are done blowing chunks.

  29. Go ahead, Jock. Explain to us how geocentrism and heliocentrism are mathematically equivalent despite what I just pointed out:

    Look at that diagram of the geocentric model, and note that the distance between the earth and the sun is never less than the distance between the earth and Venus. Then look at the other diagram and note that the distance between the earth and the sun is less than the distance between the earth and Venus for part of the year. That alone shows you that the models aren’t mathematically equivalent, and there’s plenty more where that came from.

  30. keiths: The thing that will confuse Flint is that the number 0009 on the counter is clearly a count, and it is clearly an integer. He is adamant that a count cannot possibly be a measurement, and so he will have to maintain that the surveyor’s wheel hasn’t measured anything! It’s bizarre, and it implies that surveyors are all idiots for using the wheels to determine lengths.

    I think I said the equivalent of this regarding digital instruments, several thousand posts ago. Doesn’t seem to be relevant to anything in dispute.

  31. keiths:

    Correct, and that’s exactly why astronomers ditched the geocentric model in favor of the heliocentric model. They ditched the bad model and kept the good one. Unlike Neil and Jock, they understood that the two models are fundamentally different and that the geocentric model fails while the heliocentric model succeeds.

    OK, I still don’t understand, but I might be getting closer. You appear to argue that a “geocentric model” actually presumes that the planets’ orbits are other than what they actually are – that the earth must be at the center of (technically, one of the focal points of) their elliptical orbits. Of course, no model can make this true, because it’s not. If that’s what you mean, then it’s not a matter of the model making bad predictions, it’s a matter of the failure to model reality faithfully enough to be useful.

  32. keiths:
    Some people lack good judgment, particularly after they’ve humiliated themselves in an internet debate by adopting a crackpot position they cannot defend. They become desperate to score a point.

    Ah, great to start my day with such a wonderful example of inadvertent humor. I couldn’t have said this better myself.

  33. keiths:
    keiths:

    Flint:

    Speak for yourself. I think most people — educated people, anyway — understand that 7.62, like any other real number, occupies one and only one point on the number line, just like Mrs. Bedington taught you in third grade. It is exact.

    In any case, what matters is not what most people think, but rather what is correct. Real numbers are exact by definition. I asked you a couple of days ago whether you agreed with the Britannica definition of real numbers:

    I’m still interested. Do you agree with that definition? Do you understand that “infinite decimal expansion” implies exactitude?

    Sigh. Yes, I agree that real numbers are infinitely precise. I understand that anytime YOU refer to a numerical expression as describing a real number, your intention is to communicate this.

    What Jock and I have been trying to tell you is, in real life “real” numbers as you understand them are almost never used for anything. In the “real” world, nearly EVERY number derives from either a count or a measurement. This being the case, Frank and everyone else is going to presume that if the number is not an integer, it is an approximation. Both of us made this stipulation right at the start of this discussion. We’re talking about “numbers you’d find in your inbox”, etc.

    Educated people might not understand this, but actual real people do. If your intent is not obvious (telling Frank it’s a measurement is obvious), they have enough sense to ask “where did this number come from?” We have been calling that the “provenance” of the number. And if it came from a calculation that itself involved no values derived from any measurement, people would understand that it’s exact by definition. The point is, few people are going to look at a number like 7.62 and assume an infinity of zeroes (or a repeating pattern) not in evidence. They will assume it’s a normal (as opposed to real) number, that is, a measurement-derived approximation.

  34. Flint:
    I’m still waiting for Flint and Jock to explain how they could get a measurement in my 9-ruler scenario without counting the rulers. Jock’s most recent attempts at avoiding the question were pretty lame. He said he would use a measuring tape, but of course I had already ruled that out in my scenario. There are no other measuring devices available, and the whole point is to describe how you would make the measurement using the one-foot rulers available to you.

    The obvious answer is that you count the rulers, coming up with a measurement of 9 feet. Flint and Jock don’t want to admit that, yet they haven’t come up with any other way of obtaining the measurement despite having had five and a half weeks to do so.

    Pretty funny.

    Uh, I hope you realize what you are doing here: you are setting up your problem in such a way that ANY response that isn’t exactly what you demand must be wrong. So you insist that we MUST use your rulers, and we MUST count them, and we MUST interpret the total length in terms of the count of rulers, and that count MUST be 9, because you disallow anything else.

    But we aren’t disagreeing with you because we think you’re stupid. You are doing it to yourself.

  35. DNA_Jock:
    keiths,

    Well, you just need a more predictive geocentric model, is all.
    It will be less parsimonious, of course, which drove the adoption of the heliocentric model.

    Not quite my reading of that particular history. The geocentric model they were developing wasn’t based on parsimony, it was based on religious doctrine. If I recall correctly, one of the reasons the heliocentric model was initially rejected was because it implied (due to being so much simpler) that scripture was wrong. So the coordinate system change wasn’t demanded by astronomers so much as it was blessed by the pope.

  36. Flint: Not quite my reading of that particular history.

    Both can be true. Parsimony and doctrine.

    I’m pretty sure heliocentrism was clunky before Newton.

    I don’t think epicycles went away before gravitation.

  37. Not that it matters, but IIRC, the theologically-motivated stipulation that the orbits and epicycles be PERFECT CIRCLES was the problem, and actually made the heliocentric version messier. But that’s all history. Today one can create a perfectly predictive geocentric model. Buttloads of large fictitious forces, But beware premature triumphalism, the heliocentric model also carries buttloads of smaller fictitious forces, leading to the dreaded mathematical equivalence.
    And no keiths, I erred in offering you a geocentrism cookie when you have yet to explain the difference between Karen’s error and what you did. You seem terribly eager for any digression…

  38. Flint: Uh, I hope you realize what you are doing here: you are setting up your problem in such a way that ANY response that isn’t exactly what you demand must be wrong. So you insist that we MUST use your rulers, and we MUST count them, and we MUST interpret the total length in terms of the count of rulers, and that count MUST be 9, because you disallow anything else.

    Haha, and I was wondering why he didn´t just drive to the hardware store to buy himself a tape measure. And why on earth does he have a drawer full of rulers?!? Weirdo!

  39. Flint:

    Uh, I hope you realize what you are doing here: you are setting up your problem in such a way that ANY response that isn’t exactly what you demand must be wrong. So you insist that we MUST use your rulers, and we MUST count them, and we MUST interpret the total length in terms of the count of rulers, and that count MUST be 9, because you disallow anything else.

    The entire point of the thought experiment was to leave you no recourse but to count the rulers in order to get the measurement. Count the rulers, and you get the measurement. Refuse to count the rulers, and you don’t get the measurement. Therefore you are wrong. The hard line you envision between counts and measurements does not actually exist.

    There’s a reason you and Jock avoided the question for more than five weeks (and Jock is still avoiding it). It isn’t hard to figure out what that reason is.

  40. Jock,

    If you don’t count the rulers, how do you obtain the measurement “9 feet”?

    It’s a super scary question that you’ve been avoiding for more than five weeks, but I’m asking you to summon your courage and answer it.

  41. Jock:

    Today one can create a perfectly predictive geocentric model. Buttloads of large fictitious forces, But beware premature triumphalism, the heliocentric model also carries buttloads of smaller fictitious forces, leading to the dreaded mathematical equivalence.

    The heliocentric model doesn’t require any “fictitious forces.” Gravity by itself explains the motions of the celestial bodies, and it works just fine without the aid of fictitious forces. Kepler and Newton were right. Kepler accurately described the elliptical orbits of the planets, and Newton showed how gravity explained those orbits perfectly.

    You linked to the Wikipedia article on the Tychonic system (which isn’t actually geocentric, since it has some of the planets revolving around the sun). I’ve attached an image from that article below. Take a look at that image and ask yourself: do those paths look the same as the paths in the heliocentric model? Is there any way of superimposing the Tychonic model on the heliocentric model such that the motions of the celestial bodies match? The answer is no, and it couldn’t be more obvious.

    It’s the 21st century, Jock, and we understand how the planets move. They orbit the sun, not the earth. Geocentrism and heliocentrism are not mathematically equivalent.

  42. keiths:
    There’s a reason you and Jock avoided the question for more than five weeks (and Jock is still avoiding it). It isn’t hard to figure out what that reason is.

    If it isn’t hard, why have you spent more than five weeks and you haven’t figured it out yet?

    If you put your mind to it, you can find a way to associate a count into any measurement. The fact that counts are always exact and measurements never are doesn’t ever seem to bother you at all. Weird.

  43. keiths:
    Jock,

    If you don’t count the rulers, how do you obtain the measurement “9 feet”?

    It’s a super scary question that you’ve been avoiding for more than five weeks, but I’m asking you to summon your courage and answer it.

    It’s not scary at all, once you realize that there are plenty of ways to measure a length, and the only reason you require that we use your rulers is so that you can say we’re avoiding the question if we don’t, and unwilling to see the “obvious” if we do. So we have been answering your question since the beginning, but you can’t admit it. YOUR answer, wrong as it is, is the only answer you will ever be satisfied with. No correct answer will ever suffice. We aren’t willing to pretend to be stupid to pacify your needs.

  44. keiths:

    The thing that will confuse Flint is that the number 0009 on the counter is clearly a count, and it is clearly an integer. He is adamant that a count cannot possibly be a measurement, and so he will have to maintain that the surveyor’s wheel hasn’t measured anything! It’s bizarre, and it implies that surveyors are all idiots for using the wheels to determine lengths.

    petrushka:

    I think I said the equivalent of this regarding digital instruments, several thousand posts ago.

    Yes, you did, and I made a similar point. That was weeks ago, and Jock and Flint still haven’t caught on.

    Doesn’t seem to be relevant to anything in dispute.

    It’s relevant to the topic of measurement. It’s also relevant because it gets at J&F’s weird idea that 3 and 3.0 aren’t the same number.

  45. Corneel: Haha, and I was wondering why he didn´t just drive to the hardware store to buy himself a tape measure. And why on earth does he have a drawer full of rulers?!? Weirdo!

    He could have stood the pole up next to him, and figured it was maybe 1.5 keiths. Which might very well be close enough.

  46. He is adamant that a count cannot possibly be a measurement, and so he will have to maintain that the surveyor’s wheel hasn’t measured anything! It’s bizarre, and it implies that surveyors are all idiots for using the wheels to determine lengths.

    Of course, I never said any such thing, so we have another example of having to lie to win.

    The field being surveyed is obviously one field-length long, but that unit is too nonstandard to be useful. So the goal here is to convert that unit into something standard. From there, if desired, it can be converted into any other units that may be more helpful. The wheel produces, in wheel-circumferences, a rough and ready approximation. Now, measure the circumference in standard units, do a bit of calculation, and the conversion works.

    NOTE that the measurement of the wheel is approximate, hence the measurement of the field is approximate, which means that the desired count of standard units will be approximate. There are absolutely no exact (in keithspeak, “real”) numbers involved anywhere in this exercise. And that’s the point.

    (A number of years ago, my neighbor wanted to build a fence along our mutual property line. So we both hired surveyors, who brought their wheels, did their measurements, and disagreed by two inches. They explained that over the distances measured, two inches was within their error margin. My neighbor and I split the difference, since the fence itself was over an inch thick.)

  47. Flint,

    Any normal person in my 9-ruler scenario would count the rulers and write down the measurement “9 feet”. It’s common sense. You can’t get the measurement without doing the count. If you do the count, you get the measurement.

    According to you, that should be impossible, because counts and measurements don’t mix. But it is possible, and everyone who counts the rulers and writes down the measurement proves you wrong. You seem emotionally incapable of accepting that, but it’s true. They count the rulers and they get the measurement, whether you like it or not. Your belief is false.

    You’ve been shown that your belief is wrong, but you won’t give it up. You know those religious people you disdain for hanging on to beliefs that are irrational and have been proven wrong? You are one of them. You are hanging onto a piece of dogma that has been proven wrong. It’s completely irrational.

  48. keiths:
    Flint,

    Any normal person in my 9-ruler scenario would count the rulers and write down the measurement “9 feet”. It’s common sense. You can’t get the measurement without doing the count. If you do the count, you get the measurement.

    Until the length wasn’t close to an integer number of rulers. Then suddenly your count doesn’t work, because you have to subdivide your counts into subcounts, and do this as many times as it takes to achieve the desired level of precision. Which should suggest that the length isn’t a count after all. Consider an actual count, for a change. How many jelly beans in the jar? You are allowed to dump them out and count them. How close to exact do you suppose your count would be? How would this differ from a measurement? What would qualify as “approximately” a jelly bean?

    According to you, that should be impossible, because counts and measurements don’t mix. But it is possible, and everyone who counts the rulers and writes down the measurement proves you wrong. You seem emotionally incapable of accepting that, but it’s true. They count the rulers and they get the measurement, whether you like it or not. Your belief is false.

    Your interpretation of what I’ve been saying is false. I think we know why. I’m DAMN tired of repeating that counts are exact, measurements are not. Your blockheaded determination to pretend otherwise has grown old.

    You’ve been shown that your belief is wrong, but you won’t give it up.

    It’s not a belief, it’s a mathematical fact.

    You know those religious people you disdain for hanging on to beliefs that are irrational and have been proven wrong? You are one of them. You are hanging onto a piece of dogma that has been proven wrong. It’s completely irrational.

    Been looking in the mirror again, have you? You have become a parody of yourself. Grow up.

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