Nature snapshots [10 Aug 2023]

Many gems in the 10 Aug issue I found home back from Western Canada. Starting with the cover theme related to the fascinating paper Solid-body trajectoids shaped to roll along desired pathways by Sobolev et al. which shows that there exist 3D objects corresponding to any infinitely periodic trajectory and furthermore that such objects can be printed to this effect (watch the great videos!). Although they are more likely to be of a period larger than 1, i.e. producing several copies of the trajectory basis before returning to their original contact point. Amazingly, self-intersecting trajectories may also be produced.

Plenty of AI entries, like Artificial-intelligence search engines wrangle academic literature (as an advanced Google Scholar) and Publishing companies (like Elsevier) developing ChatGPT-like search engines. (While trying to stay clear from fake references!). Plus a long enquiry on Rules to keep AI in check: nations carve different paths for tech regulation about the different approaches envisioned by the EU, the USA, and China, with little practical advance so far for the first two. (While the UK plans its own AI safety summit in Bletchley Park this Fall.)

And an article on how Chinese students are starting to feel less inclined to study abroad. And not only in connection with the COVID pandemic. Or the US growing restrictions on student visas. But mainly because of the quickly growing attractivity of mainland China and Hong Kong universities. (The article states that “For every 1,000 PhDs that have been denied [visa] by the US government, US institutions will lose nearly US$1 billion in tuition fees”, but this does not sound highly relevant since most PhD tuitions are paid from supervisors’ grants, while students from other country may substitute for those denied visa.)

nAIture

Plenty of AI related entries in Nature this week (8 June 2023):

• Why Nature will not allow the use of generative AI in images and videos (until they cannot spot them)
• AI intensifies fight against paper mills (as a further hindrance rather than an ally)
• AI learns to write sorting software on its own, through deep learning (DeepMind’s AlphaCode) for program synthesis with no training data. At a huge learning cost (31 trillion programs were tested for AlphaDev-S!). This is not a new sorting algorithm but rather a more efficient way of programming it.
• an outlier with the Golden jubilee for the Black-Scholes equation (not placing any blame on said formula for the 2008 crash) or for the emergence of disconnected-from-economics high-frequency trading)
• people, not (Google search) algorithms, choose to engage with more partisan news (as the Deep State has not yet managed to infiltrate vaccines with nano chips…!)
• how to code with ChatGPT (with the stupid line that “the tools are not as intelligent as they seem”! Well they are not at all intelligent, just produce random code with Markovian memory, deserving the sobriquet of stochastic parrots and being helped by the fact that most codes available on-line and hence in their learning database is correct)

stack overflow on strike

more [grass]hope

Following my earlier post on the terrible performances of ChatGPT for a grasshopping riddle, Bob Carpenter sent me his interaction with GPT4, using the same entry. Here is the outcome he obtained. The answer is correct, but the reasoning is wrong.

GPT4: This is a classic problem of infinite series and expected values in probability theory.

Given the nature of the grasshopper’s random walk, at each jump, it has an equal probability (1/2) of hopping to the left or to the right. Thus, we expect that, on average, it won’t be moving away from the origin (0) because the positive and negative jumps should cancel out.

However, you are asking for the expected absolute distance from the origin, which can’t be negative by definition. The key to solving this problem is to recognize that the expected value of the absolute value of a random variable is not the same as the absolute value of its expected value.

Since the absolute value function is not linear, we cannot pull the expected value inside of it. Instead, we need to directly compute the expected value of the absolute distance from the origin, which is a sum of an infinite series.

The nth jump’s absolute distance is 1/(2^n), and it has a probability of 1/2 to go either left or right. Therefore, the expected absolute distance from the origin after the nth jump is (1/2) * 1/(2^n).

Adding up these expected distances for all jumps gives us the total expected absolute distance from the origin:

E = (1/2) * (1/2 + 1/4 + 1/8 + 1/16 + …)

The sum inside the parentheses is a geometric series with a = 1/2 and r = 1/2. The sum of an infinite geometric series is a / (1 – r), so the sum of this series is (1/2) / (1 – 1/2) = 1.

Therefore, E = (1/2) * 1 = 1/2

So on average, the grasshopper is expected to be 1/2 unit away from the origin after infinitely many jumps. The expected distance it travels to return to the origin is thus 1/2 unit.

AIxcuse me?!