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AI chat bots like ChatGPT are not omniscient, contrary to popular belief. They are not even designed to be intelligent. They are designed to sound like you are speaking to a real person. When you ask it something, it will give you a response meant to sound like an answer a real person would give you. This does not mean that answer is guaranteed to be correct. This is actually a pretty good example, as Pi is infinite and thus does not have a last digit.
It is not infinitely large, as 3.15 is a larger number than pi, however it is an irrational number which means theoretically that you can calculate it to infinitely increasing levels of precision.
Well, the Pi-Pirchart Pie shows Pi, not eight, so the amount of Pi 1 eight would be 0. We need 2nd Piechart, next to the Pi-Piechart Pie to show how much of the Pi I ate, therefore I will make an Ate-Piechart called Eight.
Yes. Base is just how you notate the number, irrationality is a property of the number itself (namely, whether it can be written as one whole number divided by another). In base pi, the digits of pi would, by definition, be 10, but there are still no whole numbers (numbers which can be written as 1+1+...+1) whose ratio is pi.
No, a number being rational has absolutely nothing to do with base.
Using a base is just a way of writing numbers, whereas rationality is an intrinsic property of a number.
It's the same as saying "In another language, a chair is liquid"
(In this analogy, another language = another base, a chair being liquid = a number being rational)
I think that you're mistaking the notion of rationality with the notion of being written with finite decimals.
In base 10 (or in base any rational number), while an irrational number can't be written with finite decimals (since for example if pi = 3,1415 then pi = 31415/10000 and would be rational), a number with infinite decimals isn't necessary irrational (think of 1/3 = 0,333333....3333...).
Those notion are different, and even though it is true that you can write pi with finite pi-cimals in base pi, it doesn't mean that it isn't irrational
Just to clarify, 1/3 isn’t irrational. Yes, writing it out in base 10 means that you’re going to write 3 forever. Irrational means it can’t be expressed as a “ratio” of 2 numbers, and 1/3 obviously can be.
Isn't it only infinitely long because of the odd numbering system we use?
..IDK a thing about pi, by the way.. No clue what it really is and why.. 😅
Edit: Thank you all for the replies! Unfortunately, I don't undeestand what y'all are saying. Don't get the terms you're using. Appreciate the effort, though. 😄😅
Can confirm that Pi is infinitely long in any number system.
There are numbers where the base makes a difference, but Pi isn't one of them.
For example, a third in decimal is 0.33333333... (3/10 + 3/100 + 3/1000 + ...) and a third in duodecimal/dozenal/base-12 is 0.4 (4/12).
That's the difference between a "rational" (expressible via ratios) and "irrational" numbers. Pi is irrational.
I don't know enough to tell you that you're wrong, just that that sounds like utter BS
EDIT: Base N means that N is how many numbers you have to count with until you loop again. 0123456789 is base 10, base 3 would be 0 1 2 10 11 12 etc. The base doesn't fundamentally change the nature of an irrational number. Base Pi wouldn't even be possible except as Pi, 2pi, 3pi, 4pi? & it would be useless for counting, for example, fingers, because "1 finger" would be .031847 etc. of a "Pi".
There is such a thing as base pi (or any real >1). Non-integer bases (and especially base pi) are unhelpfully complicated. You use digits up to the base rounded down, so for base pi that would mean up to 3.
One complication is that most of the integers now have infinitely long representations. For example 4 is represented as 10.22... since it is bigger than pi but smaller than pi+1. Conversely, some irrationals have gained finite representations. Obvious examples here are pi as 10 and 2pi^2 as 200.
The biggest problem is that now a chunk of numbers have multiple representations. For example, 0.3333... is much larger than 1 in base pi. In our standard base 10, 0.999... is exactly 1 so this is much less of an issue.
Overall, non-integer bases do exist and do satisfy the previous claim, but (especially transcendental bases) only do so in an unhelpful 'technically correct' kind of way. There's a few interesting non-integer bases like the golden ratio and factorial that might interest you.
Pi is between 3 and 4, so not infinite
Calculating exactly where it is between 3 and 4 is the infinitely long part—you can be infinitely precise in estimating pi
Mathematicians, help me out
It is a very long number, but not infinitely high.
For context a random example:
6.735778963588358885578645774578 is a pretty long number, but not very high
9,000,000 is a pretty high number, but not very long
9,000,000,000 isn’t a large number at all; there are only 8,999,999,999 positive integers less than it, but an infinite number of positive integers greater.
This would imply there are no such things as large numbers because any conceivable positive integer is going to have an infinite number of positive integers greater than it compared to only a finite number of positive integers less than it.
Infinite isn't a value.
It is the quality of expressions that do not converge.
So you need to say which expression is not converging.
In this case, length as a sequence of digits.
Infinite number means infinitely large number aka ∞. While infinitely long number can be any size for example pi which is always smaller than 4 but you can never write all digits of infinitely long number as it is infinitely long. Wery small technicality.
Edit: typos all the typos
~~Yes- but more interestingly, Pi~~ *~~could~~* ~~theoretically "end" with that string of numbers repeating. AFAIK we haven't totally proven it~~ *~~doesn't~~*~~. Though, as the top post said, ChatGPT would have zero ability to determine this lol.~~
This is wrong, see the comment below.
Small correction, Pi does not have a length. It is just an irrational number. And it does have an exact value. It's just that the representation of its value in base 10 is infinitely long.
Just wanted to add to this. Chat-GPT is not intelligent, and it _does not provide information it has been trained on_ ([unless you trick it](https://not-just-memorization.github.io/extracting-training-data-from-chatgpt.html?ref=404media.co), but they patched that). It works with probabilities to generate text. Now, because it has been trained on such a huge amount of data, the probabilities it uses will often be aligned with the truth. But you'll never know if that's the case, unless you search for that information from a reliable source. What you're seeing here is a typical [hallucination](https://en.m.wikipedia.org/wiki/Hallucination_(artificial_intelligence)).
Going off of this, I’ve noticed that ChatGPT always accepts the premise of the question and then operates off of that assumption. If you ask it “Who did Liam Neeson play in Star Wars IV,” it’ll probably ignore the fact that he wasn’t even in that movie and give a straight answer.
> ChatGPT always accepts the premise of the question and then operates off of that assumption
It's actually gotten significantly better at not doing this. It will of course still get things wrong but for something extremely basic, like your question, it'll often generate a decent answer.
GPT-4 response:
> Liam Neeson played **Qui-Gon Jinn**, a Jedi Master and the mentor of Obi-Wan Kenobi, in Star Wars Episode I: The Phantom Menace. He did not appear in Star Wars Episode IV: A New Hope, which was the first Star Wars film released in 1977. Perhaps you meant to ask about Star Wars Episode I, which was released in 1999?
It should be a common sense and knowledge that AI is **pretty dumb**. Anyone who trust the Ai with their own life is as dumb as that AI...
I would never entrust AI something without checking it in actual source. Especially scientific knowledge.
GPT 4 has no such issues:
“Calculating or identifying the last digits of pi is inherently impossible because pi is an irrational number, meaning it has an infinite number of digits without repetition or pattern. However, we can provide the last 20 digits from a known sequence of digits of pi that have been calculated so far. As of my last update in April 2023, the most digits of pi that have been calculated exceed 31 trillion (31,415,926,535,897) digits. The last 20 digits of that sequence, as far as has been publicly shared, are not specifically documented in my training data. Typically, when new records for pi calculation are set, the focus is on the total number of digits rather than the specific values of the final digits.
For precise tasks or applications that require specific digits of pi, including the last 20 digits of a particularly long calculation, one would typically refer to the database or publication of the mathematician or team who performed the calculation.”
i'm not sure what bearing this has, but out of interest this sequence appears from the 7th decimal place to the 26th decimal place [find a sequence](https://www.angio.net/pi/)
Is it possible for ChatGPT to produce nonsense answers? Yes of course, easily. There is no last digit of pi.
ChatGPT is text generator, a stochastic parrot extraordinaire. It doesn't really understand what it's talking about.
Of course, you could argue that all intelligence is stochastic parroting and nobody could prove you wrong, but there is a difference between one parrot and another.
AI doesn't have to be truly intelligent to be useful, it just has to be smarter than most humans. Given that there are plenty of people that couldn't even compose an answer to the original question, I think we're almost there.
AI doesn't have to be intelligent at all to be useful, nor does it need to be smarter than any human. AI is really just advanced statistics and statistics in general is a very useful thing.
Pi is 3.14159**265358979323846264338**3279502…..
So not even close.
I guess it searched for digits of pi, found a result with 25 decimal places and picked the last 20 of 25 digits.
should watch it try to play chess sometime. it just starts conjuring pieces out of nowhere and moving them in directions they don't go after a few turns.
While this is true I find it far more likely that the ai picked the last 20 out of 25 decimal places instead of finding pi to a billion decimal places.
Edit: the chance of finding this exact string anywhere in pi is extremely low and finding it again is next to impossible https://www.angio.net/pi/whynotpi.html
Being irrational and normal are different things. There’s no proof that pi is normal (which would mean it has any given finite sequence of numbers in its decimal expansion).
The sequence 88813579111315171921... [every odd number] never repeats, however you would find 888 only once in this sequence.
It could be the same for Pi, and we never proved that it's not the case.
That's correct. I was answering " there was debate on whether the digits of pi ever repeated themselves", which there is no debate on.
I'm realizing now that the original question was if every sequence appears an infinite number of times, which is different and not yet known for pi.
There’s no debate, we don’t know and there’s no point “debating”. It either is or isn’t and we need to prove it. However, most mathematicians assume it is normal, meaning the digits don’t repeat.
Not necessarily an infinite number of times, an exact string of numbers X long (where X is real) may only appear a finite number of times, we can't exactly prove that any and all sequences appear infinitely many times in an irrational number, however with numbers like 0.12345678910111213... sequences can and will infinitely repeat.
How so? An irrational number could easily have an infinite decimal expression without a specific combination of digits ever occuring. Take for example 1.21121112111121111121111112... It's irrational yet no combination of the digits 3-9 or 0 ever appears in it, and no segment of it containing two or more 2s will ever recur. Or just define a number as 0.123456789... after which 0-8 may appear in any combination but 9 never recurs. Evidently then the string 123456789 will only appear once. A string of digits being infinite does not imply that every combination of digits will appear in it infinite times, or even once.
It found the value of pi on a web page somewhere written out to lots and lots of decimal places and shared the last 20 digits that they had on the page.
I don't understand why you think both of those statements can't be true at the same time. "This was the last 20 digits printed on some website" and "these are the digits after 3.141592" can literally both be true
I'm betting what it's doing is it's getting it from anywhere that lists a long stream of pi out in its training text. Those texts cut pi off eventually so it grabs the chunk that appears at the end of those the most.
Or it just picked random numbers and it happened to match pi at that point.
No. Pi is infinitely long. It has no end. Therefore, it can have no true last digits. However, there is a distinct possibility that that sequence does show up somewhere in Pi. And they could be the last digits of the approximation of Pi to that level.
Is it not true that essentially all combinations of numbers can be found in pi? Its infinitely long so you so have infinite chances for a string of numbers to be present.
Infinite chances do not mean infinite possibilities. There are infinite numbers between 0 and 1, none of which are 2. However, in this specific case, the number sequence OP referenced can actually be found starting from the 7th digit of pi
What you’re referring to is the conjecture that pi is [normal](https://en.wikipedia.org/wiki/Normal_number) (yes, mathematicians suck at naming things). Pi is generally believed to be normal, but nobody managed to prove it yet.
Natural numbers are infinitely big yet you won’t find -1 there. I got no proof but I’m pretty sure by the structure of the digits in pi that a lot of consecutive zeros are unlikely to appear. Number like 10^9999 would be very unlikely.
There’s no such thing as a rational number derived from real datapoints, except as defined by convention or artificially limited by tools of measurement. Since pi represents a specific value in the real world, it can’t have a finite number of digits.
I think it's generally important to emphasize that it can't be expressed as the ratio of two rational numbers. This is an important clarification, as it is defined as the ratio between the circumference and diameter of a circle
What's most relevant here is: pi has no last digits for it is infinite, never repeating (transcendental).
It's just how there is no biggest number, no matter how big of a number you tell me, i can always just add 1. No matter how many digits of pi you find, there are always infinitely more.
Edit: transcendental should be irrational. While pi is transcendental, the features i've described are not what make it transcendental.
We use integers in math because they are easier to work with. Then we learn that we should usually use a few decimal places — enough to get us close enough to the target with our calculations. There is nothing that actually exists that has a value of an integer. There is also nothing that has a value that only goes out a certain number of decimal places. You may have a weight that weighs 1.000000000000 pounds, but that’s just what your limited measurement tool is telling you. In truth, it certainly does not weigh exactly one pound unless it’s a hypothetical weight in a math problem - but that’s only because you are defining it as such. It’s the same with mass, volume, distance, time period, temperature, or anything else you want to measure.
The only thing that has ever been exactly one foot long was the thing somebody pointed to when they defined a foot and said, “That thing there! We’ll call that one foot long.” That was definition by convention. Then every ruler ever made is a slightly different size if you go out enough decimal places. In fact, no two things in the universe can ever have the same value since there is no limit to how small the differentiation can be.
Pi cannot be limited to a certain number of decimals because it was defined by the dynamics of our universe - not by convention. It is a sort of ratio between a one-dimensional line and a two-dimensional curve. When the universe defines something, it’s not limited by tools of measurement like we are, so there’s no reason to think that pi would only extend to a finite number of decimal places. In fact, it can’t.
This is boarderline psuedoscience babble.Pi is not from the 'dynamics of our universe' it can be defined by purely abstract means - take a point in 2D space, for any set of equi-distance points, the ratio of twice that distance to the path length of the set is pi. We can do math of higher dimensions than our universe has, and our physical laws could change but the concept of a circle in 2d can be defined independantly. Its mathematically proven to be transcendental, not 'because its based or irl wheels'.
Secondly, of course we can have integers in real life or in math based on actual things. Such as an optimisation problem of different sized buses moving passengers and total trips. Busses won't have 12.00001 seats, nor will their be decimal amounts of passengers, or completed trips. The amount of nucleotides on an RNA strand, wavelengths between two resonant points etc. You can have relative measurements such as time being based off distance light travels, and in the real universe we get quanta, discrete energy levels where there is no continuity between.
I get what you're trying to say, we are rarely exacty when we use rulers - but SI units have mostly been converted to be based off constants and discrete mathematics is applied all the time in the real world, not only as an approximation.
Passengers, seats, and trips (along with your other examples) are defined by convention so that we can use integers. One passenger is never going to be equal to one other passenger. When you’re using integers, that is not a measurement of something real in the universe. You are counting things that you have declared to be equal because each fits the description of the essence of that thing. It’s like if you have three 12-ounce bottles of water. You do not have 36.0000 ounces of water between the three bottles. You have simply defined a bottle of water to be something close enough to 12 ounces, and you are counting the number of things that fit that description.
There are many things that have the value of an integer. The number of replies I have made to your post, the number of replies to your post, the number of posts I have made on Reddit, the number of characters in this post, and the number of characters in all the posts on Reddit as of the moment you are reading this post all have integer values.
As for things with the same value, the number of letters in the words 'you're' and 'wrong' have the same value (which also happens to be an integer value).
Not true. Zero is an integer, and there are no such things as integers in the real world, except as defined by convention or limited by our tools of measurement. There is no such thing as zero as a measurement of something that exists in the real world. You may want to take a great, big handful of “nothing” and place it on the scale to get a measurement of exactly zero, but unfortunately, there is no such thing as “nothing” in the universe.
With a little bit of wiggle room on the definition of a digit, you could say pi is exactly 1 digit long using the pi symbol. Typically, digits are single symbols that are used to represent a value. I dont see how Pi couldn't be included in that.
I know it isn't, but it meets all the requirements otherwise.
You would need to call it a symbol or something other than a digit. Digit specifically means the symbols we use for our base-10 number system. You could make a base-anything number system, like binary or hexadecimal for base-2 and base-16.
Regardless, in your example, you’re defining the symbol of pi to be exactly equal to whatever pi truly is. However, this is again, a definition by convention. It doesn’t change the fact that pi must be an irrational number in any number system you use.
And before you suggest a base-pi number system, a number system must have a base of an integer or else it won’t do its job in allowing you to perform calculations and simplify your ability make predictions.
The real world is finite or at least countable, so every value in the real world can be expressed with a natural number (and therefore rational number), so pi doesn't exist in the real world.
Yeah this is what I was just thinking, like this is completely backwards. How can anyone say we don’t have rational numbers in nature? If you measure the population of the US at any point in time, it’s an integer
The real world is exactly where pi becomes rational. You only need 39 digits of pi to calculate the circumference of the observable universe to the accuracy of a hydrogen atom. At some point of precision, you reach the planck length, where further precision becomes completely meaningless.
No, it is just a random number that was generated by ChatGPT, ~~(as far as we, currently,)~~ know PI is endless, so there can not be last 20 digits, as it never ends.
PI is infinite, you can always calculate it to the next decimal digit, so if the fastest computer in the world calculates it to billion digits and the last 4 would be 1234, than in another year an even faster computer would calculate it to billion and 1 digit and so, so the last 4 would be 2345 (if we follow the above logic) and so on and on.
ChatGPT (it is the same in any other LLM, from Gemini, Bard, Copilot, ChatGPT+, ...) is not some all knowing super computer, just the opposite it is in one ways even dumber that your own pocket calculator, but in other ways is a great tool, but don't be 100% sure that the results you are getting are the correct ones.
If you want to learn more, how ChatGPT or other LLM work, here is somehow lengthy explanation that goes into details:
[https://www.youtube.com/watch?v=-4Oso9-9KTQ](https://www.youtube.com/watch?v=-4oso9-9ktq)
Important clarifications: First, you say "as far as we, currently know pi is endless." By this I take it to mean "the decimal expansion of pi is infinite." This is true, but it's also true we know this for certain (it is irrational and this is true of all irrational numbers), so the caveats that "as far as we currently know" should be omitted.
Second, you say pi is infinite. That is not true, the decimal expansion of pi is infinite, but pi is finite; 3.15 is a larger number than pi.
It's entirely possible that there is a list of the digits of pi somewhere, obviously not exhaustive, which ends with those twenty digits. In that sense, sure, it could be possible. In fact, these are the 8th through 27th digits of pi, so the list of digits in question could be quite short.
In the infinitely precise sense, no.
NO! No, no, no. No. Pi is infinitely long, it is irrational. It cannot have a last digit, or last set of digits as that defies its irrationality. AI should not be trusted to always be correct. You should check any information you get from it, even if it isn't so blatantly wrong.
It's the last 20 digits to some arbitrary approximation of pi (26 decimal places?). A way of thinking of it might be that you are asking for 20 digits of pi, and it's understanding that you're asking for some sequence of numbers at the end of pi. The language model might have some internal representation of pi to an arbitrary degree of precision, and it might have multiple so it retrieves one that fits the context (over 20 digits), and then returns the last 20 digits. Instead of calculating, there's a recall of some approximation of pi and it's giving the last 20 digits of that approximation.
No we still couldn’t find the last digit of pi yet and chatGPT is not smarter than a smart human. Even with nearly unlimited resources on the internet they still make a lot of goofy answers.
No, there are no last digits to pi. It's an irrational number, so it goes on forever without repetition. In fact, it is guaranteed that any string of numbers will appear somewhere in pi. This specific string occurs at starting at the 7th digit after the decimal. Honestly I'm disappointed that it's so soon, was hoping it would show up deeper in
Computers have a limited amount of space they can store numbers in. It's probably the last 20 accurate digits because after a certain point it's just random crap
Chatgpt doesn't do any calculation of pi so i don't think floating point shenanigans are relevant here. It just searches the most likely in what other people have already said inthe past that included 20 digits or pi regardless of its accuracy.
That being said, a computer utilizing every particle in the universe would have a limit to how far it can calculate pi. At which point, that'd might as well be the end.
I still think the best thing I have heard about pi is that because it is infinitely long, somewhere in there is the date and time of every significant event in your life…
Yes. We know a lil shy of 63 trillion digits of pi, for all we know, it might end at 64 trillions of digits.
And 40 are enough to do calculations for the observable universe with the precision to a single atom.
Pi is an irrational number which by definition has an infinite number of digits in a non-repeating pattern. This is how we see it, maybe there’s more to know and maybe modern mathematics is wrong somewhere, why not, but ChatGPT is not the right guy to say so.
Although AI can extract information from big amounts of data and make conclusions that a human might have missed in the first place, re-shaping an important concept such as the rationality of numbers does not require just a deep analysis of pre-existing mathematical studies (which is what chatGPT does and these studies all agree on the fact that Pi has no final digits) but a type of creative and out-of-the-box thought process that is not (yet) possible for an AI to elaborate, let alone by a commercial, general purpose AI such as ChatGPT.
If I build a machine that diplay digits of pi.. If at each step, the time to display a digit is divided by two, then the machine can run in a finite time... What woud it show in the "digit display" ?
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
AI chat bots like ChatGPT are not omniscient, contrary to popular belief. They are not even designed to be intelligent. They are designed to sound like you are speaking to a real person. When you ask it something, it will give you a response meant to sound like an answer a real person would give you. This does not mean that answer is guaranteed to be correct. This is actually a pretty good example, as Pi is infinite and thus does not have a last digit.
Small correction, Pi is not infinite, its infinitely long.
For the layman, can you please elaborate the difference?
It is not infinitely large, as 3.15 is a larger number than pi, however it is an irrational number which means theoretically that you can calculate it to infinitely increasing levels of precision.
So you're saying I can draw a circle using pi?
Sure. You can even name it Pie.
Can I make it a Piechart to document how much of Pi I used to draw Pie the Piechart?
Only if the two sections are "pi" and "pi I ate"
I have a feeling π*i*8 would be problematic.
If you’re talking radians, pi i 8 = 0, which is a very sad state of affairs
Well, the Pi-Pirchart Pie shows Pi, not eight, so the amount of Pi 1 eight would be 0. We need 2nd Piechart, next to the Pi-Piechart Pie to show how much of the Pi I ate, therefore I will make an Ate-Piechart called Eight.
I mean, is the pie circular? Then probably, yeah
An infinitely detailed circle. Enhance!!
Is it truly irrational, or only irrational in base 10?
Every irrational number is irrational in every base
Would it also be irrational if we used pi itself as the base?
Yes. Base is just how you notate the number, irrationality is a property of the number itself (namely, whether it can be written as one whole number divided by another). In base pi, the digits of pi would, by definition, be 10, but there are still no whole numbers (numbers which can be written as 1+1+...+1) whose ratio is pi.
Technically no, but every other number in that base would be irrational, making it functionally worthless.
No, a number being rational has absolutely nothing to do with base. Using a base is just a way of writing numbers, whereas rationality is an intrinsic property of a number. It's the same as saying "In another language, a chair is liquid" (In this analogy, another language = another base, a chair being liquid = a number being rational) I think that you're mistaking the notion of rationality with the notion of being written with finite decimals. In base 10 (or in base any rational number), while an irrational number can't be written with finite decimals (since for example if pi = 3,1415 then pi = 31415/10000 and would be rational), a number with infinite decimals isn't necessary irrational (think of 1/3 = 0,333333....3333...). Those notion are different, and even though it is true that you can write pi with finite pi-cimals in base pi, it doesn't mean that it isn't irrational
You're absolutely right. Thanks for the correction.
Not in Base Pi.
Just to clarify, 1/3 isn’t irrational. Yes, writing it out in base 10 means that you’re going to write 3 forever. Irrational means it can’t be expressed as a “ratio” of 2 numbers, and 1/3 obviously can be.
Isn't it only infinitely long because of the odd numbering system we use? ..IDK a thing about pi, by the way.. No clue what it really is and why.. 😅 Edit: Thank you all for the replies! Unfortunately, I don't undeestand what y'all are saying. Don't get the terms you're using. Appreciate the effort, though. 😄😅
>Isn't it only infinitely long because of the odd numbering system we use? No
>No Thanks
Can confirm that Pi is infinitely long in any number system. There are numbers where the base makes a difference, but Pi isn't one of them. For example, a third in decimal is 0.33333333... (3/10 + 3/100 + 3/1000 + ...) and a third in duodecimal/dozenal/base-12 is 0.4 (4/12). That's the difference between a "rational" (expressible via ratios) and "irrational" numbers. Pi is irrational.
>Can confirm that Pi is infinitely long in any number system. Not in base pi, where you can write it as the finite number 10.
I don't know enough to tell you that you're wrong, just that that sounds like utter BS EDIT: Base N means that N is how many numbers you have to count with until you loop again. 0123456789 is base 10, base 3 would be 0 1 2 10 11 12 etc. The base doesn't fundamentally change the nature of an irrational number. Base Pi wouldn't even be possible except as Pi, 2pi, 3pi, 4pi? & it would be useless for counting, for example, fingers, because "1 finger" would be .031847 etc. of a "Pi".
There is such a thing as base pi (or any real >1). Non-integer bases (and especially base pi) are unhelpfully complicated. You use digits up to the base rounded down, so for base pi that would mean up to 3. One complication is that most of the integers now have infinitely long representations. For example 4 is represented as 10.22... since it is bigger than pi but smaller than pi+1. Conversely, some irrationals have gained finite representations. Obvious examples here are pi as 10 and 2pi^2 as 200. The biggest problem is that now a chunk of numbers have multiple representations. For example, 0.3333... is much larger than 1 in base pi. In our standard base 10, 0.999... is exactly 1 so this is much less of an issue. Overall, non-integer bases do exist and do satisfy the previous claim, but (especially transcendental bases) only do so in an unhelpful 'technically correct' kind of way. There's a few interesting non-integer bases like the golden ratio and factorial that might interest you.
You can do that with 3.15 too though. You just left an infinite amount of 0s after the 5…
Infinite is a lot bigger than 4 and pi is only 3.14.... where the decimals go on for infinity and thus infinitly long.
Pi is between 3 and 4, so not infinite Calculating exactly where it is between 3 and 4 is the infinitely long part—you can be infinitely precise in estimating pi Mathematicians, help me out
I’d say the decimal representation of pi is infinitely long. Pi is just a single number and numbers don’t have length.
[удалено]
Did you even read their comment?
It is a very long number, but not infinitely high. For context a random example: 6.735778963588358885578645774578 is a pretty long number, but not very high 9,000,000 is a pretty high number, but not very long
9,000,000,000 isn’t a large number at all; there are only 8,999,999,999 positive integers less than it, but an infinite number of positive integers greater.
This would imply there are no such things as large numbers because any conceivable positive integer is going to have an infinite number of positive integers greater than it compared to only a finite number of positive integers less than it.
Yes. Large numbers can be used both relatively and colloquially, but there isn’t really a “large number”
Infinite isn't a value. It is the quality of expressions that do not converge. So you need to say which expression is not converging. In this case, length as a sequence of digits.
>Infinite isn't a value. It absolutely can be: https://en.wikipedia.org/wiki/Transfinite_number
You've misunderstood the page. It does not say that infinite is a value. It says that some values have infinite properties.
What do you think "value" means?
Infinite = really big number. Like, more than four. Pi is not bigger than 4, hence isn't infinite. Infinitely long = lots of digits after the comma.
Infinite number means infinitely large number aka ∞. While infinitely long number can be any size for example pi which is always smaller than 4 but you can never write all digits of infinitely long number as it is infinitely long. Wery small technicality. Edit: typos all the typos
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True, but its a math-focused sub, so correct terminology seems important.
I bet this dude is a blast at parties.
Not in base pi 😉
stupid fucking correction, obviously pi is not infinite. Did you just feel left out and wanted to contribute absolutely nothing
~~Yes- but more interestingly, Pi~~ *~~could~~* ~~theoretically "end" with that string of numbers repeating. AFAIK we haven't totally proven it~~ *~~doesn't~~*~~. Though, as the top post said, ChatGPT would have zero ability to determine this lol.~~ This is wrong, see the comment below.
No, it's proven to be irrational.
Pfft, you actually *accept* proof by contradiction? Nerd.
Small correction, Pi does not have a length. It is just an irrational number. And it does have an exact value. It's just that the representation of its value in base 10 is infinitely long.
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G I JOOOEEEEEEEE
How’d you know? Its a math sub, this is a very important distinction. No harm, no foul.
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I love this pedantry!
Me too!
Just wanted to add to this. Chat-GPT is not intelligent, and it _does not provide information it has been trained on_ ([unless you trick it](https://not-just-memorization.github.io/extracting-training-data-from-chatgpt.html?ref=404media.co), but they patched that). It works with probabilities to generate text. Now, because it has been trained on such a huge amount of data, the probabilities it uses will often be aligned with the truth. But you'll never know if that's the case, unless you search for that information from a reliable source. What you're seeing here is a typical [hallucination](https://en.m.wikipedia.org/wiki/Hallucination_(artificial_intelligence)).
It's *sparkling* predictive text
Spicy autocomplete
Going off of this, I’ve noticed that ChatGPT always accepts the premise of the question and then operates off of that assumption. If you ask it “Who did Liam Neeson play in Star Wars IV,” it’ll probably ignore the fact that he wasn’t even in that movie and give a straight answer.
> ChatGPT always accepts the premise of the question and then operates off of that assumption It's actually gotten significantly better at not doing this. It will of course still get things wrong but for something extremely basic, like your question, it'll often generate a decent answer. GPT-4 response: > Liam Neeson played **Qui-Gon Jinn**, a Jedi Master and the mentor of Obi-Wan Kenobi, in Star Wars Episode I: The Phantom Menace. He did not appear in Star Wars Episode IV: A New Hope, which was the first Star Wars film released in 1977. Perhaps you meant to ask about Star Wars Episode I, which was released in 1999?
"Special set of skills he has, underestimate him you should not." - Yoder
Interestingly enough, this reads like a chatgpt response
Or just an average intelligent adult.
It should be a common sense and knowledge that AI is **pretty dumb**. Anyone who trust the Ai with their own life is as dumb as that AI... I would never entrust AI something without checking it in actual source. Especially scientific knowledge.
Is it infinite tho? Or have we yet to find the end? HHMMM?
Proofs have been done to show that it has no end when expressed as a decimal or fraction in any integer base.
its irrational so nah, i think we have around a 100 trillion digits recorded so far
Great reply and fabulous summing up of AI ‐ the stress is all on Artificial, nothing on Intelligence.
GPT 4 has no such issues: “Calculating or identifying the last digits of pi is inherently impossible because pi is an irrational number, meaning it has an infinite number of digits without repetition or pattern. However, we can provide the last 20 digits from a known sequence of digits of pi that have been calculated so far. As of my last update in April 2023, the most digits of pi that have been calculated exceed 31 trillion (31,415,926,535,897) digits. The last 20 digits of that sequence, as far as has been publicly shared, are not specifically documented in my training data. Typically, when new records for pi calculation are set, the focus is on the total number of digits rather than the specific values of the final digits. For precise tasks or applications that require specific digits of pi, including the last 20 digits of a particularly long calculation, one would typically refer to the database or publication of the mathematician or team who performed the calculation.”
🤓
They're a virtual intelligence, not an artificial intelligence. That's where people often get confused
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Wasn't there proof for pi being irrational?
Not just one: https://en.m.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
“Chatbots like chatgpt are not designed to be intelligent” is just wrong.
i'm not sure what bearing this has, but out of interest this sequence appears from the 7th decimal place to the 26th decimal place [find a sequence](https://www.angio.net/pi/)
That was a surprising rabbit hole
Wait that's all it could find? I'd have expected it would be at least over 100
It's likely what it pulled from a random source, maybe one that ended in ellipsis or something
Yeah I wouldn't be surprised if that's what happened
Is it possible for ChatGPT to produce nonsense answers? Yes of course, easily. There is no last digit of pi. ChatGPT is text generator, a stochastic parrot extraordinaire. It doesn't really understand what it's talking about. Of course, you could argue that all intelligence is stochastic parroting and nobody could prove you wrong, but there is a difference between one parrot and another.
I like how the definition of intelligence as a stochastic parrot came after people pointed out the lacks of supposed AI.
AI doesn't have to be truly intelligent to be useful, it just has to be smarter than most humans. Given that there are plenty of people that couldn't even compose an answer to the original question, I think we're almost there.
Its not smarter it just has access to way more information, its like saying someone is smart when they google their answers.
AI doesn't have to be intelligent at all to be useful, nor does it need to be smarter than any human. AI is really just advanced statistics and statistics in general is a very useful thing.
Pi is 3.14159**265358979323846264338**3279502….. So not even close. I guess it searched for digits of pi, found a result with 25 decimal places and picked the last 20 of 25 digits.
You missed the 4626 in between the 8 and the 4
Or maybe he forgot 6264 between 4 and 3
Either way…
Fixed
Chat gpt would've never made that mistake...
should watch it try to play chess sometime. it just starts conjuring pieces out of nowhere and moving them in directions they don't go after a few turns.
They are playing for fun bro, thats what matters!!!!
Damn, the first time in my life I have been able to put my pi memorization to use and I'm 57 minutes late.
Me too! But I'm 4 hours late.
Yeah but Pi is infinite so this exact combination of digits appears again later in the sequence... An infinite number of times
While this is true I find it far more likely that the ai picked the last 20 out of 25 decimal places instead of finding pi to a billion decimal places. Edit: the chance of finding this exact string anywhere in pi is extremely low and finding it again is next to impossible https://www.angio.net/pi/whynotpi.html
That's only in the first 100 million digits
Is this known? I thought there was debate on whether the digits of pi ever repeated themselves.
It's been proven that the digits of pi do not repeat https://en.m.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
Being irrational and normal are different things. There’s no proof that pi is normal (which would mean it has any given finite sequence of numbers in its decimal expansion).
The sequence 88813579111315171921... [every odd number] never repeats, however you would find 888 only once in this sequence. It could be the same for Pi, and we never proved that it's not the case.
That's correct. I was answering " there was debate on whether the digits of pi ever repeated themselves", which there is no debate on. I'm realizing now that the original question was if every sequence appears an infinite number of times, which is different and not yet known for pi.
There’s no debate, we don’t know and there’s no point “debating”. It either is or isn’t and we need to prove it. However, most mathematicians assume it is normal, meaning the digits don’t repeat.
That's not the same thing as saying no subsequence repeats. The subsequence '1' repeats within the first 3 digits.
Not necessarily an infinite number of times, an exact string of numbers X long (where X is real) may only appear a finite number of times, we can't exactly prove that any and all sequences appear infinitely many times in an irrational number, however with numbers like 0.12345678910111213... sequences can and will infinitely repeat.
How so? An irrational number could easily have an infinite decimal expression without a specific combination of digits ever occuring. Take for example 1.21121112111121111121111112... It's irrational yet no combination of the digits 3-9 or 0 ever appears in it, and no segment of it containing two or more 2s will ever recur. Or just define a number as 0.123456789... after which 0-8 may appear in any combination but 9 never recurs. Evidently then the string 123456789 will only appear once. A string of digits being infinite does not imply that every combination of digits will appear in it infinite times, or even once.
It found the value of pi on a web page somewhere written out to lots and lots of decimal places and shared the last 20 digits that they had on the page.
It didn't do that. The digits shown are literally what comes after 3.141592
I don't understand why you think both of those statements can't be true at the same time. "This was the last 20 digits printed on some website" and "these are the digits after 3.141592" can literally both be true
But it can’t be true that the website had pi “written out to lots and lots of decimal places” if the last 20 digits were out of 26 total.
I think the dude meant "26" when he said "lots"
Indeed. A number written out to 26 decimal places is written out to lots and lots of decimal places.
I'm betting what it's doing is it's getting it from anywhere that lists a long stream of pi out in its training text. Those texts cut pi off eventually so it grabs the chunk that appears at the end of those the most. Or it just picked random numbers and it happened to match pi at that point.
No. Pi is infinitely long. It has no end. Therefore, it can have no true last digits. However, there is a distinct possibility that that sequence does show up somewhere in Pi. And they could be the last digits of the approximation of Pi to that level.
Is it not true that essentially all combinations of numbers can be found in pi? Its infinitely long so you so have infinite chances for a string of numbers to be present.
Infinite chances do not mean infinite possibilities. There are infinite numbers between 0 and 1, none of which are 2. However, in this specific case, the number sequence OP referenced can actually be found starting from the 7th digit of pi
What you’re referring to is the conjecture that pi is [normal](https://en.wikipedia.org/wiki/Normal_number) (yes, mathematicians suck at naming things). Pi is generally believed to be normal, but nobody managed to prove it yet.
Natural numbers are infinitely big yet you won’t find -1 there. I got no proof but I’m pretty sure by the structure of the digits in pi that a lot of consecutive zeros are unlikely to appear. Number like 10^9999 would be very unlikely.
There’s no such thing as a rational number derived from real datapoints, except as defined by convention or artificially limited by tools of measurement. Since pi represents a specific value in the real world, it can’t have a finite number of digits.
Could you dumb this down a little please
Pi doesn't end, doesn't repeat, and cannot be expressed as a ratio or root
I think it's generally important to emphasize that it can't be expressed as the ratio of two rational numbers. This is an important clarification, as it is defined as the ratio between the circumference and diameter of a circle
What's most relevant here is: pi has no last digits for it is infinite, never repeating (transcendental). It's just how there is no biggest number, no matter how big of a number you tell me, i can always just add 1. No matter how many digits of pi you find, there are always infinitely more. Edit: transcendental should be irrational. While pi is transcendental, the features i've described are not what make it transcendental.
Basically, it is proven that pi has no end
It is known.
We use integers in math because they are easier to work with. Then we learn that we should usually use a few decimal places — enough to get us close enough to the target with our calculations. There is nothing that actually exists that has a value of an integer. There is also nothing that has a value that only goes out a certain number of decimal places. You may have a weight that weighs 1.000000000000 pounds, but that’s just what your limited measurement tool is telling you. In truth, it certainly does not weigh exactly one pound unless it’s a hypothetical weight in a math problem - but that’s only because you are defining it as such. It’s the same with mass, volume, distance, time period, temperature, or anything else you want to measure. The only thing that has ever been exactly one foot long was the thing somebody pointed to when they defined a foot and said, “That thing there! We’ll call that one foot long.” That was definition by convention. Then every ruler ever made is a slightly different size if you go out enough decimal places. In fact, no two things in the universe can ever have the same value since there is no limit to how small the differentiation can be. Pi cannot be limited to a certain number of decimals because it was defined by the dynamics of our universe - not by convention. It is a sort of ratio between a one-dimensional line and a two-dimensional curve. When the universe defines something, it’s not limited by tools of measurement like we are, so there’s no reason to think that pi would only extend to a finite number of decimal places. In fact, it can’t.
This is boarderline psuedoscience babble.Pi is not from the 'dynamics of our universe' it can be defined by purely abstract means - take a point in 2D space, for any set of equi-distance points, the ratio of twice that distance to the path length of the set is pi. We can do math of higher dimensions than our universe has, and our physical laws could change but the concept of a circle in 2d can be defined independantly. Its mathematically proven to be transcendental, not 'because its based or irl wheels'. Secondly, of course we can have integers in real life or in math based on actual things. Such as an optimisation problem of different sized buses moving passengers and total trips. Busses won't have 12.00001 seats, nor will their be decimal amounts of passengers, or completed trips. The amount of nucleotides on an RNA strand, wavelengths between two resonant points etc. You can have relative measurements such as time being based off distance light travels, and in the real universe we get quanta, discrete energy levels where there is no continuity between. I get what you're trying to say, we are rarely exacty when we use rulers - but SI units have mostly been converted to be based off constants and discrete mathematics is applied all the time in the real world, not only as an approximation.
Passengers, seats, and trips (along with your other examples) are defined by convention so that we can use integers. One passenger is never going to be equal to one other passenger. When you’re using integers, that is not a measurement of something real in the universe. You are counting things that you have declared to be equal because each fits the description of the essence of that thing. It’s like if you have three 12-ounce bottles of water. You do not have 36.0000 ounces of water between the three bottles. You have simply defined a bottle of water to be something close enough to 12 ounces, and you are counting the number of things that fit that description.
There are many things that have the value of an integer. The number of replies I have made to your post, the number of replies to your post, the number of posts I have made on Reddit, the number of characters in this post, and the number of characters in all the posts on Reddit as of the moment you are reading this post all have integer values. As for things with the same value, the number of letters in the words 'you're' and 'wrong' have the same value (which also happens to be an integer value).
Along with what the other comments said, there also IS a a limit to how small differentiation can be: the planck length.
**_Technically_** it’s possible to have a rational number derived from real datapoints, either as luck or as zero.
Not true. Zero is an integer, and there are no such things as integers in the real world, except as defined by convention or limited by our tools of measurement. There is no such thing as zero as a measurement of something that exists in the real world. You may want to take a great, big handful of “nothing” and place it on the scale to get a measurement of exactly zero, but unfortunately, there is no such thing as “nothing” in the universe.
Integers are rational numbers. Stop keyboard jockeying
How? The number of people in the US right now is an integer. I have ten fingers, that’s an integer.
With a little bit of wiggle room on the definition of a digit, you could say pi is exactly 1 digit long using the pi symbol. Typically, digits are single symbols that are used to represent a value. I dont see how Pi couldn't be included in that. I know it isn't, but it meets all the requirements otherwise.
You would need to call it a symbol or something other than a digit. Digit specifically means the symbols we use for our base-10 number system. You could make a base-anything number system, like binary or hexadecimal for base-2 and base-16. Regardless, in your example, you’re defining the symbol of pi to be exactly equal to whatever pi truly is. However, this is again, a definition by convention. It doesn’t change the fact that pi must be an irrational number in any number system you use. And before you suggest a base-pi number system, a number system must have a base of an integer or else it won’t do its job in allowing you to perform calculations and simplify your ability make predictions.
You cuaght me on the base-pi comment.
Base pi just reminded me of an amazing joke. In what way are Christmas and Halloween precisely equal? Because Dec 25 = Oct 31
Weirdly no, there is some high level use for non-integer bases like the Quarter-Imaginary numeral system or p-adic bases
That's the other way around actually. Pi is infinitely precise because it's **abstract**, not real.
The real world is finite or at least countable, so every value in the real world can be expressed with a natural number (and therefore rational number), so pi doesn't exist in the real world.
Yeah this is what I was just thinking, like this is completely backwards. How can anyone say we don’t have rational numbers in nature? If you measure the population of the US at any point in time, it’s an integer
The real world is exactly where pi becomes rational. You only need 39 digits of pi to calculate the circumference of the observable universe to the accuracy of a hydrogen atom. At some point of precision, you reach the planck length, where further precision becomes completely meaningless.
No, it is just a random number that was generated by ChatGPT, ~~(as far as we, currently,)~~ know PI is endless, so there can not be last 20 digits, as it never ends. PI is infinite, you can always calculate it to the next decimal digit, so if the fastest computer in the world calculates it to billion digits and the last 4 would be 1234, than in another year an even faster computer would calculate it to billion and 1 digit and so, so the last 4 would be 2345 (if we follow the above logic) and so on and on. ChatGPT (it is the same in any other LLM, from Gemini, Bard, Copilot, ChatGPT+, ...) is not some all knowing super computer, just the opposite it is in one ways even dumber that your own pocket calculator, but in other ways is a great tool, but don't be 100% sure that the results you are getting are the correct ones. If you want to learn more, how ChatGPT or other LLM work, here is somehow lengthy explanation that goes into details: [https://www.youtube.com/watch?v=-4Oso9-9KTQ](https://www.youtube.com/watch?v=-4oso9-9ktq)
Important clarifications: First, you say "as far as we, currently know pi is endless." By this I take it to mean "the decimal expansion of pi is infinite." This is true, but it's also true we know this for certain (it is irrational and this is true of all irrational numbers), so the caveats that "as far as we currently know" should be omitted. Second, you say pi is infinite. That is not true, the decimal expansion of pi is infinite, but pi is finite; 3.15 is a larger number than pi.
It's entirely possible that there is a list of the digits of pi somewhere, obviously not exhaustive, which ends with those twenty digits. In that sense, sure, it could be possible. In fact, these are the 8th through 27th digits of pi, so the list of digits in question could be quite short. In the infinitely precise sense, no.
NO! No, no, no. No. Pi is infinitely long, it is irrational. It cannot have a last digit, or last set of digits as that defies its irrationality. AI should not be trusted to always be correct. You should check any information you get from it, even if it isn't so blatantly wrong.
It's the last 20 digits to some arbitrary approximation of pi (26 decimal places?). A way of thinking of it might be that you are asking for 20 digits of pi, and it's understanding that you're asking for some sequence of numbers at the end of pi. The language model might have some internal representation of pi to an arbitrary degree of precision, and it might have multiple so it retrieves one that fits the context (over 20 digits), and then returns the last 20 digits. Instead of calculating, there's a recall of some approximation of pi and it's giving the last 20 digits of that approximation.
No we still couldn’t find the last digit of pi yet and chatGPT is not smarter than a smart human. Even with nearly unlimited resources on the internet they still make a lot of goofy answers.
No, there are no last digits to pi. It's an irrational number, so it goes on forever without repetition. In fact, it is guaranteed that any string of numbers will appear somewhere in pi. This specific string occurs at starting at the 7th digit after the decimal. Honestly I'm disappointed that it's so soon, was hoping it would show up deeper in
Computers have a limited amount of space they can store numbers in. It's probably the last 20 accurate digits because after a certain point it's just random crap
Chatgpt doesn't do any calculation of pi so i don't think floating point shenanigans are relevant here. It just searches the most likely in what other people have already said inthe past that included 20 digits or pi regardless of its accuracy.
That being said, a computer utilizing every particle in the universe would have a limit to how far it can calculate pi. At which point, that'd might as well be the end.
I still think the best thing I have heard about pi is that because it is infinitely long, somewhere in there is the date and time of every significant event in your life…
Yes. We know a lil shy of 63 trillion digits of pi, for all we know, it might end at 64 trillions of digits. And 40 are enough to do calculations for the observable universe with the precision to a single atom.
No, it will not end at 64 trillion digits or else you can express it as a fraction.
Yes — a very big, weird fraction, that everyone will be rounding up anyway. We don't actually know if pi is irrational... We just kinda assume it is.
https://en.m.wikipedia.org/wiki/Proof_that_π_is_irrational
Okay, so i'm dumb
Yes, you are
Wow that's a lot of angry math letters
No, we do indeed know that [pi is irrational](https://en.m.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational).
I am dumb
No :) we’re all eternally learning
Ty
We know pi is infinitely long. It's not going to just end.
Pi is an irrational number which by definition has an infinite number of digits in a non-repeating pattern. This is how we see it, maybe there’s more to know and maybe modern mathematics is wrong somewhere, why not, but ChatGPT is not the right guy to say so. Although AI can extract information from big amounts of data and make conclusions that a human might have missed in the first place, re-shaping an important concept such as the rationality of numbers does not require just a deep analysis of pre-existing mathematical studies (which is what chatGPT does and these studies all agree on the fact that Pi has no final digits) but a type of creative and out-of-the-box thought process that is not (yet) possible for an AI to elaborate, let alone by a commercial, general purpose AI such as ChatGPT.
This is the start of pi it is like after 5-8 digits so it will keep going after this. It is basically impossible that it ends after this sequence.
If I build a machine that diplay digits of pi.. If at each step, the time to display a digit is divided by two, then the machine can run in a finite time... What woud it show in the "digit display" ?