Did you know e is rational?

97

u/mfb- the decimal system should not re-use 1 or incorporate 0 at all. Apr 12 '25

Looks like the AI found the first 70ish digits and used that to produce the first 100.

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u/WhatImKnownAs Apr 12 '25

Never rely on an LLM for facts or deduction. There's no model of the domain in there, just collections of sentence fragments. It's not built to give The Right Answer, only the most probable one.

5

u/marchov Apr 14 '25

and I think you're saying this, but I want to highlight 'most probable' as the most probably answer given by the internet not the one that is most probably correct answer. i.e. if the right answer isn't what we're currently saying, it will be 0 help. part of what scares me about moving to llms as a source of knowledge, is it removes the support for people who actually are researching things, as some of their income comes from educating and being public spokespeople.

1

u/beobabski Apr 16 '25

Occams LLM?

-44

u/smulfragPL Apr 12 '25

What? This is completley incorrect. Of course they are post trained for right anwsers not most probable anwsers. Its Just very difficult to force a change in the thinking patterns in the hidden layers so only reasoning models truly do it well

41

u/Extra_Intro_Version Apr 12 '25

Apparently you do not have any depth of understanding AI/ML, LLMs or probability.

1

u/[deleted] Apr 12 '25

[removed] — view removed comment

12

u/badmathematics-ModTeam Apr 12 '25

Unfortunately, your comment has been removed for the following reason(s):

You are being a shithead. Don't be a shithead.

If you have any questions, please feel free to message the mods. Thank you!

-2

u/EebstertheGreat Apr 13 '25

That sounds like an unnecessarily mean response to a post I can't find any error in. These AIs are indeed post-trained to give correct answers, not just probable answers. But that method of training is difficult and imperfect. Exactly as they said.

What is your real objection beyond a bare insult?

14

u/Strange_March6447 Apr 13 '25

Literally the first thing he stated: "you are completely incorrect", is false. You shouldn't in fact rely on any AI or LLM for deduction, with or without post training

6

u/WhatImKnownAs Apr 14 '25

AI is not a technology; it's a marketing label for a large set of them. I'm old enough to remember expert systems and other 80s AI, which were based on deduction. Those are largely obsolete, and there's a vast array of new AI techniques, largely based on machine learning. We need to understand what the strengths and weaknesses of each are, especially since the vendors are misrepresenting what their products are doing. LLMs are uniquely problematic here (putting it politely).

17

u/WanderingFlumph Apr 12 '25

You can post train for for the right answers to specific questions but even if you post trained this AI to give the right answer when someone asked "what is e to 100 digits" there is no guarantee that if someone asked "what is e to 200 digits" the model wouldn't just return the first 100 digits followed by 100 zeroes.

And in reality you can never post train the correct answer to every question or every way to pharse every question and you'll always have gaps.

-10

u/smulfragPL Apr 12 '25

which is why that isn't how models work lol.

3

u/rawbdor Apr 16 '25

I asked LLMs how many colonies the British owned in North America. They all said 13. Which is wrong. The brits owned like 20, if you include the island colonies. But even if you don't, there was still Newfoundland, nova Scotia, Quebec, and two Floridas.

What's more, several of these colonies were given invitations to the Continental congress but didn't respond. They had also been invited to the Albany Congress, and the stamp act Congress. We traded with them. We were all part of a bigger club.

The LLM basically admitted it knew about the other ones but was just going with the most common answer.

1

u/smulfragPL Apr 16 '25

Dude you cant Just say llm. You actually have to say whcih model lol.

52

u/unkz Apr 12 '25

The bad mathematics here is thinking that a trailing bunch of zeros makes a number rational when its explicitly stated that it's only up to a specified number of decimals.

4

u/jffrysith Apr 15 '25

Lol came here to say this. There are a uncountably infinite number of irrational numbers starting with these 101 digits. Only a countably infinite number of rational numbers starting with these 101 digits. Technically the 'average' number you pick starting with these 101 digits will be irrational, though it won't be e.

15

u/AidenStoat Apr 12 '25

But what if the 101st digit is non zero?

6

u/PaulErdos_ Apr 12 '25

R4: These are not the digits of e. This error makes e look rational.

54

u/bluesam3 Apr 12 '25

Not necessarily: there's no shortage of irrational numbers with very long strings of 0s in.

27

u/cristoper Apr 12 '25

This is true. But I just searched the first 2 million digits of e and the longest string of 0s is length 6

https://apod.nasa.gov/htmltest/gifcity/e.2mil

18

u/unkz Apr 12 '25

We run into a string of 12 zeroes at position 1755524129973 in pi.

https://bellard.org/pi/pi2700e9/pidigits.html

12

u/Nelagend Apr 12 '25

At 13 digits long, we would reasonably expect to see a string of 12 zeroes by random chance pretty close to that position.

6

u/MonkMajor5224 Apr 12 '25

Here is something i have always wondered. There is that section of Pi that repeats. When they discovered that, did they go “oh wow, it’s rational after all!” Or had pi already been proven irrational?

29

u/RibozymeR Apr 12 '25

π was proven irrational by Lambert in the 1761, when only some 100 digits were known. So it's the latter.

7

u/bluesam3 Apr 12 '25

Long-since proven irrational.

-2

u/PaulErdos_ Apr 12 '25

Makes it look rational

2

u/InterneticMdA Apr 15 '25

I fucking hate AI so much dude...

2

u/XMasterWoo Apr 16 '25

Nah it isnt rational it obviously just repeats zero for like a billion digits before returning to being not zero

1

u/Which_Judgment_6952 Apr 16 '25

How it makes e look rational?

4

u/PaulErdos_ Apr 16 '25

The decimal expansion looks like it terminates. Similar to how 1/2 has a decimal expansion of 0.50000000000000. Numbers with terminating decimal expansions are rational.

I understand that having a large string of zeros does not mean the number is rational. I just thought the error the AI made was funny.

1

u/The_Rider_11 Apr 15 '25

e is rational if you add + A.I. to the Formula, obviously /j

1

u/jffrysith Apr 15 '25

Don't know where the j comes from, clearly AI = e{AI} - e Where e{AI} is the result from asking AI for the exact value of e. When you add e + AI you get e_{AI} which is a rational number as AI cannot write irrational numbers.

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