Dear Vaughan, Of course you're right. But if the journalist had explained what a topos is, it might rather have destroyed his thesis that topos theory is a "magic bullet" which is going to solve all the problems of AI. I suppose it does no harm if people at Huawei believe that; and if it causes them to throw money at people doing research in topos theory, so much the better. But I remain sceptcal. I'm reminded of the occasion when Guerino Mazzola decided that topos theory was the "magic bullet" that would solve all the problems of musical analysis, and wrote a big book to prove his point: nothing much came of that in the long term. Peter Johnstone ________________________________ From: Vaughan Pratt <pratt@cs.stanford.edu> Sent: 02 September 2024 06:32 To: Wesley Phoa <doctorwes@gmail.com> Cc: categories@mq.edu.au <categories@mq.edu.au> Subject: Re: Grothendieck in the Guardian "I’m relieved the journalist didn’t try to explain what a topos was, or indeed anything mathematical." Why would anyone object to journalists doing exactly those things? Do we want to keep mathematics a dark secret, or what? A topos is simply one of many possible generalization of sets and their functions that allows many other mathematical objects besides sets to be imbued with some of the essential properties that make sets so valuable in mathematics. For example graphs and their maps form a topos with very similar properties to sets and their functions, such as having the notion of a power set. But not all properties, for example the law of the excluded middle, which holds for sets but not graphs. Vaughan Pratt On Sun, Sep 1, 2024 at 1:16 PM Wesley Phoa <doctorwes@gmail.com<mailto:doctorwes@gmail.com>> wrote: Thanks - I saw this! I’m relieved the journalist didn’t try to explain what a topos was, or indeed anything mathematical. Sent
On Aug 31, 2024, at 1:13 PM, Paul Taylor <categories@paultaylor.eu<mailto:categories@paultaylor.eu>> wrote:
An article about Alexander Grothiendieck has just appeared in the Guardian online newspaper. Be warned, it contains some seriously weird stuff! Toposes get a mention, though "not as we know them", along with Huawei, AI and Olivia Caramello. Beyond that, I'm not going to comment!
Since Microsoft mangles web addresses, here is the address with the punctuation removed:
www theguardian com science article 2024 aug 31 alexander-grothendieck-huawei-ai-artificial-intelligence
Paul Taylor.
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________________________________ From: Vaughan Pratt <pratt@cs.stanford.edu> Sent: 02 September 2024 06:32 To: Wesley Phoa <doctorwes@gmail.com> Cc: categories@mq.edu.au <categories@mq.edu.au> Subject: Re: Grothendieck in the Guardian "I’m relieved the journalist didn’t try to explain what a topos was, or indeed anything mathematical." Why would anyone object to journalists doing exactly those things? Do we want to keep mathematics a dark secret, or what? A topos is simply one of many possible generalization of sets and their functions that allows many other mathematical objects besides sets to be imbued with some of the essential properties that make sets so valuable in mathematics. For example graphs and their maps form a topos with very similar properties to sets and their functions, such as having the notion of a power set. But not all properties, for example the law of the excluded middle, which holds for sets but not graphs. Vaughan Pratt On Sun, Sep 1, 2024 at 1:16 PM Wesley Phoa <doctorwes@gmail.com<mailto:doctorwes@gmail.com>> wrote: Thanks - I saw this! I’m relieved the journalist didn’t try to explain what a topos was, or indeed anything mathematical. Sent
On Aug 31, 2024, at 1:13 PM, Paul Taylor <categories@paultaylor.eu<mailto:categories@paultaylor.eu>> wrote:
An article about Alexander Grothiendieck has just appeared in the Guardian online newspaper. Be warned, it contains some seriously weird stuff! Toposes get a mention, though "not as we know them", along with Huawei, AI and Olivia Caramello. Beyond that, I'm not going to comment!
Since Microsoft mangles web addresses, here is the address with the punctuation removed:
www theguardian com science article 2024 aug 31 alexander-grothendieck-huawei-ai-artificial-intelligence
Paul Taylor.
----------
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