Changing the last one to r=80 instead of r=40, GPT4o ends up saying:
> The circles overlap in certain areas, depending on their size and position, creating a layered visual effect where the largest circle (third one) dominates most of the canvas space.
Though tbf to it, I'm not sure I'd say this looks like MM either: https://i.imgur.com/0VHdocf.png (unless I knew this was the intent prior).
GPT4o certainly gave it a good go (prompt: "What cartoon character would you say this SVG code renders most closely to?"). That's maybe a little too "prompting" tbf:
"""
The SVG code you provided creates an image with three circles:
A large circle at the center (at coordinates 100, 100) with a radius of 50.
Two smaller circles at the top left (at coordinates 50, 50) and top right (at coordinates 150, 50) with a radius of 40 each.
This configuration closely resembles the head and ears of Mickey Mouse. The larger circle represents the head, and the two smaller circles represent the ears.
"""
Slightly more generic prompt: "What is this code drawing? Can you suggest what it might be representing?"
"""
What It Might Represent:
Mickey Mouse Head: The arrangement resembles a simplified "Mickey Mouse" head, where the large central circle represents the head, and the two smaller circles represent the ears.
Abstract Art: Alternatively, it could be an abstract design with three overlapping circles of different sizes, suggesting some form of simple geometric art.
The circles are positioned such that the smaller ones are symmetrically placed above the larger central one, which is a typical representation of a head with ears.
"""
And more generic "I've been sent this code, what is it drawing?" ends with:
"""
You will see three overlapping circles. The largest circle is near the center, while two smaller circles are positioned above and slightly to the left and right of the center. The arrangement may resemble a basic representation of a Mickey Mouse head shape, with the large circle as the face and the two smaller circles as ears.
"""
I appreciate you giving multiple examples including an extremely surprising failure given the other successes without assuming malice on my part in asking.
I can agree with that, this is the primary textbook for the Open University's (excellent) Galois Theory MSc course (https://www.open.ac.uk/postgraduate/modules/m838. I really enjoyed my time on that course.
I was also very interested in reading about the the original papers prior to the various advancements in mathematical thinking and notation that tend to reframe how the theory is taught today. For that I highly recommend Peter Neumanns "The mathematical writings of Evariste Galois" (https://ems.press/books/hem/102) – it has the french side by side with a direct English translation along with notes explaining the context and possible thought process (it also served as a fun way to read some more French whilst I was trying to learn the language).
I hope it's OK to hijack the thread a bit: could you please tell me whether you'd recommend the Open University?
I think I might be interested in one of their Mathematics MSc. I don't know anyone personally who's gone so I'd love to hear what you thought of the experience please.
Yes, I would certainly recommend them if you are personally motivated. I've previously studied at Imperial for my BEng and then did a Mathematics BSc and then followed up with an MSc with the OU and certainly as a mature student, I have loved my time with the OU.
You get out of it very much what you put in. The materials on the undergrad side are excellent, at the MSc level you will basically be given a list of textbook resources, the odd OU prepared summary material and then a few online video tutorials (live) and then you get on with it.
There are forums and you have direct contact with your tutor though speaking myself, I never really engaged with them. You'll have a few "TMAs" to do (tutor marked assignments) and that's where you'll get direct feedback on your approach and questions but you are encouraged to message tutors if you need some guidance, and when I have I have always had a good experience.
My email is in my bio if you want to reach out, I'd be happy to send you some of the M838 course notes for you to get an idea of what you can expect.
The Game of Life is a 2-dimensional cellular automata (CA), so given the 1-dimensional rule 110 has been proven to be universal / Turing-complete [1], it becomes less mysterious. Albeit the complexity of the system required to set it up to do anything "useful" would be prohibitive.
I'm currently finishing up my OU MSc and the project I picked was specifically around cellular automata - only in this case relating to them calculating any arbitary automatic sequence - which are sequences you can create from finite state machines - that really opened my eyes to the fact these sorts of very, very simple machines can, with the right (and rather complex) setup, be made to do pretty much whatever you want from a computational PoV. In that paper by Rowland and Yassawi they give a constructive proof to calculate the required update rules for a CA that outputs any particular automatic sequence. That itself gives some hints at some ways of deriving the input and rules for these systems to do some particular job. [2]
I know Wolfram often gets dunked on for ego/hubris but in Chapter 11 of a New Kind Of Science he goes into how the Rule 110 CA can be setup to "calculate" (output) other CAs. From there it starts to become a little less mysterious that these systems can generate behaviour you could imagine running on a CPU of some sort.[3]
I bought one of these, and really like it. My main issue would be is the mechanism is a little chunky so I resorted to blue-tacking a dice on the wall towards the bottom of it so that it's flush [1]. The width of a normal sized dice was pretty much perfect to get it sitting "straight" against the wall, without that it would tilt downwards - and that was driving me nuts.
Re. materials & quality - it looks and feels very good to me,
the print is very sharp, it is smooth and well made - no sharp edges or fraying, nothing is peeling off etc. For the price I am very happy. I have no nostalgia for the acorn nor a need for a second clock but would be tempted if I could get away with it in the kitchen.
They must've partnered because I bought mine originally from RetroFied [2] - I saw it mentioned by Neil on an RMC video at the time and thought I must get one for the price (£25).
I've been using GPT-4 to help me understand my MSc mathematics course and I've noticed this sort of stuff more and more as I start to look at the answers, always confidently written, in detail.
Way back when GPT was just fresh on the scene I had terrible anxiety about "what is the point of my whole career or even learning any more" but these days I'm much less concerned. I'll ask it something relatively simple, like "make a sentence out of words 'a', 'b', & 'c'" for it to reply with "'a' 'b' 'd' 'e'" for me to then correct it with "oh, you didn't use c" for it to then respond "sorry, here - 'a', 'c', 'd', 'f'" etc.
Definitely an amazing complimentary tool but when they say "can make mistakes, check important..." that's essential.
This sort of issue holds with all kinds of prompts, on both platforms. I most recently (to test Bard's image generation capabilities) was asking Bard/Gemini to generate home designs using highly specific prompts -- layout of the house, materials for the facade, window placement and style, etc -- and it was shocking how frequently it would just ignore critical pieces of the prompt, and then continue to ignore when corrected.
I think it might be in reference to the semi-frequent heists that happen, that have real monetary value behind them. EVE players seem to be a special breed. Some of the stories are pretty incredible.
> The circles overlap in certain areas, depending on their size and position, creating a layered visual effect where the largest circle (third one) dominates most of the canvas space.
Though tbf to it, I'm not sure I'd say this looks like MM either: https://i.imgur.com/0VHdocf.png (unless I knew this was the intent prior).