Random numbers (e.g. from PRNGs) are everywhere in AI—but are they actually a good idea? In particular, are random numbers the best we can do for numerical problems like linear algebra, integration and optimisation? Probabilistic Numerics (PN) has (very radical!) views 🧵 In numerical integration, e.g. estimating ∫_{-3}^{3} f(x) dx, one popular approach is Monte Carlo (named after the casino), which uses random numbers to select the locations x_i of evaluations f(x_i).

The PN approach to numerical integration is called Bayesian quadrature (BQ).

People who say that AI could not possibly kill us all seem very confident about the geopolitical relationships between states that have invested a lot in both AI and nuclear weapons Even if AI does not "press the button", the rapidly-advancing, uncertain, progress of AI might threaten the balance of peace e.g. AI-powered underwater drones that prove capable of locating nuclear submarines—then a state might think it could launch a successful first strike

My views on covid seem to have become a bit, well—radical. Please allow me to explain. I did not start out radical. I am lucky to have a settled, establishment-adjacent, career. Three years ago, on the eve of the pandemic, I trusted the establishment. I trusted the establishment when it said that there was ~no covid in Oxford in Mar 20. Then our little family all got it. I trusted the establishment when it said that, because we were healthy, we'd be fine. I trusted the establishment when it said kids don't get sick

You can't judge a Twitter fiction account by a single tweet any more than you can judge a novel(la) by fifty of its words. You have to read for a while to absorb the voice, the themes, the trajectories. Nonetheless, here's a sampler of tweets from my favourite fiction accounts:

https://twitter.com/ctrlcreep/status/1305366807352672258?s=46&t=t0TAmDxGrzCT9CTpoSuhbA

It's Sunday—porridge day! Porridge, my (slightly-sticky) emotional crutch. I'm going to document my porridge with photos, in the hope that you may be able to share in my enjoyment.

- 125g salted butter
- 250g jumbo rolled oats
- 1.75L milk
- 1 tsp salt 1. *Fry the oats in butter* in a frypan

I may be the only person alive holding these three beliefs simultaneously:

3. Covid is actually very bad
2. AI poses a potentially-existential threat
1. Random numbers are a bad idea for computation My beliefs on random (including pseudo-random) numbers are spelt out in our book: probabilistic-numerics.org/textbooks/

Most are not OK with eating a raw egg because of the 1 in 20,000 risk of Salmonella—which causes diarrhoea & vomiting.

Most seem OK with getting covid (when triply-vaccinated) despite the **1 in 20** risk of #LongCovid—which causes diarrhoea, vomiting, BRAIN DAMAGE & much more The 1 in 20 risk is derived from @ONS data.

https://twitter.com/dr2nisreenalwan/status/1548959952923918337

What is Probabilistic Numerics (PN)? To illustrate, take one core use case of PN— computing integrals. Most integrals are intractable (life is hard), so we must often integrate numerically. Sadly, numerical integrators are unreliable & computationally expensive.

PN can help! 🧵 Consider

F = ∫_{-3}^{3} f(x) dx
f(x) = exp(-(sin 3x)^2 - x^2)

The integrand f(x) here is simple—~20 characters, only atomic functions, can be evaluated in nanoseconds. However—the integral F is intractable! Let's try to calculate F numerically using PN.

When I got #LongCovid in March 2020, I was 38 and healthy. If you are anything like I was then, it is hard to understand how bad Long Covid is. I think that we all have an instinct to just… look away. But, please, it is important that you look. 1/15 My own low-points: early on, I collapsed, shaking, and was taken to A&E in an ambulance. A year later, I did not have the energy to leave the house. Formerly, I was a marathon runner, but I brought on a bad relapse with a 700m walk. Many people have it much, much, worse. 2/

I have now been sick with #longcovid for almost a year—below, some reflections on my convalescence. (1/10) While remaining mostly functional, in many ways, I'm more sick in 2021 than I was in 2020. Two weeks ago, when I last felt well enough to walk outside, I managed only 0.7km before the post-exertional malaise came on: brain fog, fatigue, pain in my neck and arm. (2/10)

Long COVID is nasty, but it is also really *weird*. (1/6) 1. My eyesight had always been fine, but became progressively worse after falling ill. Everything looked blurry. It got to the point where I maxed out the text size on all my devices. Then: over the course of two weeks, it: just got better! (2/6)

If you doubt expert forecasts of the future of work, you might like Appendix A of our 2017 report (robots.ox.ac.uk/~mosb/public/p…): we present results using only raw extrapolation of employment trends.

This extrapolation is much more optimistic than our forecasts using experts. The horizontal (x) axis of the plot is the probability of an occupation having a higher share of employment in 2030 than in 2017. The vertical (y) axis is employment, or the number of jobs.