As a teenager and an undergraduate, I sometimes experienced an unusual mental state when studying mathematics. This was a state of great happiness and seemed to arise when I was engaged in deep, deductive thinking – for instance, after spending days or weeks attempting to prove or disprove some mathematical statement. The state only arose when I was doring pure mathematics – ie, the theory of mathematics, not its application. It never lasted long – perhaps an hour, at most – and only happened a few times a year. The state did not always arrive, and I never determined what in particular I did, if anything, to provoke it. It was one of the key reasons that I decided to major in pure math at university. For ease of reference, I will refer to this state as one of deductive bliss.
Author Archive for peter
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The nature of musical scores
Is a classical musical score more like a novel or a play? In other words, is a score like the text of a novel or poem, whose meaning, at least in principle, is given by the words themselves, and not by how someone reads or declaims those words? Or is a score like the script for a play or a film, where the meaning is only realized in performance, with different performances possibly evoking very different meanings?
Concert Concat 2026
This post is one in a sequence which lists (mostly) live music I have heard, as best as memory allows. I write to have a record of my musical experiences and so these entries are intended as postcards from me to my future self. All opinions are personal.
Other posts in this collection can be found here. The most recent prior post in this sequence is here.
AI Hallucinations
Anyone trying to integrate Generative AI using Large Language Models into some commercial or professional business process should understand the dangers of so-called hallucinations. Because LLMs are generating the next text, given a corpus of training text and prompt data, all activity by these models is the same – prediction of the most highly likely completion text. Some outputs may appear to be hallucinatory only to those of us tethered to a real world. Anyone untethered – and this includes the LLMs themselves – will not be able to distinguish so-called real from so-called hallucinations, just as a sleeper cannot tell if his or her dreams are plausible or not.
Doing and thinking
Someone once said that computer programming is 10% syntax and 90% thinking. Here is Andrej Karpathy with a similar thought, writing on Twitter:
You could see it as there being two modes in creation. Borrowing GAN terminology:
1) generation and
2) discrimination.
e.g. painting – you make a brush stroke (1) and then you look for a while to see if you improved the painting (2). these two stages are interspersed in pretty much all creative work.
Palindrome week
Using the common American date format (month-day-year) this week contains ten successive palindromic dates:
5/20/25
5/21/25
5/22/25
5/23/25
5/24/25
5/25/25
5/26/25
5/27/25
5/28/25
5/29/25
Note that, although widespread in North America, this format is not compliant with the ISO Standard for formats of dates, ISO 8601.
To liberate our talents & uplift our horizons
The inspiring vision of the Australian Labor Party in their successful campaign for the Australian Federal election of 2 December 1972 (from the campaign speech of Gough Whitlam, leader of the ALP):
Our program has three great aims. They are:
– to promote equality
– to involve the people of Australia in the decision-making processes of our land
– and to liberate the talents and uplift the horizons of the Australian people.We want to give a new life and a new meaning in this new nation to the touchstone of modern democracy – to liberty, equality, fraternity.”
Delivered at Blacktown Civic Centre, Western Sydney, 13 November 1972. Source: Museum of Australian Democracy (Old Parliament House).
Musical performance
Nat King Cole:
I’m an interpreter of stories. When I perform, it’s like sitting down at my piano and telling fairy stories.”
Two nations under God
To people familiar with the organized, formal factions of the Australian Labor Party, the divisions within the Roman Catholic Church may look quite unprofessional. To an outside observer, there appear to be two main factions in the modern Church, although neither is organized or formal (as far as I know). Their names are my own invention.
Thinking aloud
For some years, I have been arguing that music is a form of thinking. (See prior posts here, published in 2011, and here, 2010.) I realize that this statement would likely be obvious to most musicians, but I still receive push-back to it from those people (especially many philosophers) who believe that thinking requires words. In this belief, they are mistaken. Even with other forms of thinking (geometric, visual, musical, kinetic, etc), though, we may still need words to explain our thinking to others.