purplecat: Hand Drawn picture of a Toy Cat (ai)
We (meaning my research group) have recently become interested in "ethical autonomy". From our point-of-view our interest is quite prescribed. Having formalised the "rules of the air" and created autonomous programs that can be shown to obey them we then got faced with the issue of when you want a pilot to deliberately break the rules of the air because there is some compelling ethical reason to do so (one of the examples we look at is when another aircraft is failing to obey the rules of the air, potentially maliciously, by moving left to avoid a collision instead of moving right. If the autonomous pilot continues to move right then eventually the two planes will collide where a human pilot would have deduced the other aircraft was breaking the rules and eventually would have moved left instead, thus breaking the rules of the air but nevertheless taking the ethical course of action).

Since ethical autonomy is obviously part of a much wider set of concerns my boss got involved in organising a seminar on Legal, Ethical, and Social Autonomous Systems as part of a cross-disciplinary venture with the departments of Law, Psychology and Philosophy.

It was an interesting day. From my point of view the most useful part was meeting Kirsten Eder from Bristol. I knew quite a bit about her but we'd not met before. She's primarily a verification person and her talk looked at the potential certification processes for autonomous systems and pointed me in the direction of Runtime Verification which I suspect I shall have to tangle with at some point in the next few years.

There was a moment when one of the philosophers asserted that sex-bots were obviously unethical and I had to bite my tongue. I took the spur of the moment decision that arguing about the ethics of what would, presumably, be glorified vibrators with a philosopher while my boss was in the room was possibly not something I wanted to get involved in.

The most interesting ethical problem raised was that of anthropomorphic or otherwise lifelike robots. EPSRC have, it transpires, a set of roboticist principles which include the principle: "Robots are manufactured artefacts: the illusion of emotions and intent should not be used to exploit vulnerable users." The problem here is that there is genuine therapeutic interest in the use of robots that mimic pets to act as companions for the elderly, especially those with Alzheimers. While this is partially to compensate for the lack of money/people to provide genuine companionship, it's not at all clear-cut that the alternative should be rejected out of hand. Alan Winfield, who raised the issue and helped write EPSRC's set of principles, confessed that he was genuinely conflicted about the ethics here . In the later discussion we also strayed into whether the language of beliefs, desires and intentions used to describe cognitive agent programs, also carried with it the risk that people would over-anthropomorphise the program.
purplecat: Hand Drawn picture of a Toy Cat (mathematics)
As you do, I remarked in passing to my in-laws that infinity plus one was not the same as one plus infinity. This gem of wisdom was duly repeated by my niece and nephew to their mathematics teacher who retorted that I was wrong and, moreover, there was no such thing as infinity. I was therefore requested, in turn, to provide a one page explanation* which could be shown to said mathematics teacher.

Now, it must be said, I don't like to undermine the fine teachers of mathematics who, I suspect, have a hard enough job as it is performing their task without random aunts interfering. On the other hand, a challenge has been laid down.

First of All, Wittgenstien )

So, physically speaking, the mathematics teacher is correct. There is no such thing as infinity. However I bet he's going to teach his class about imaginary numbers at some point and they don't exist either.

Secondly, Transfinite Mathematics )

footnotes )

This entry was originally posted at http://purplecat.dreamwidth.org/34109.html.
purplecat: Hand Drawn picture of a Toy Cat (mathematics)
As you do, I remarked in passing to my in-laws that infinity plus one was not the same as one plus infinity. This gem of wisdom was duly repeated by my niece and nephew to their mathematics teacher who retorted that I was wrong and, moreover, there was no such thing as infinity. I was therefore requested, in turn, to provide a one page explanation* which could be shown to said mathematics teacher.

Now, it must be said, I don't like to undermine the fine teachers of mathematics who, I suspect, have a hard enough job as it is performing their task without random aunts interfering. On the other hand, a challenge has been laid down.

First of All, Wittgenstien )

So, physically speaking, the mathematics teacher is correct. There is no such thing as infinity. However I bet he's going to teach his class about imaginary numbers at some point and they don't exist either.

Secondly, Transfinite Mathematics )

footnotes )

MP40

Jul. 6th, 2009 12:28 pm
purplecat: Hand Drawn picture of a Toy Cat (Default)
40 Years ago Oxford decided to offer a degree in Mathematics and Philosophy. This weekend past there were celebrations.

Talks, The Somerville Maths and Philosophers and an amusing anecdote about Hilbert under the cut )
purplecat: Hand Drawn picture of a Toy Cat (ai)
I just picked out of my work pigeonhole a package with Swedish Stamps. My address is hand-written as is a note in one corner which says "Will tell you more when I return!"

Inside is a slim volume entitiled "Being or Nothingness" by Joe K

The author, you will note, is an anagram of Joke.

There is a sticker on the cover which says "Warning! Please study the letter to Professor Hofstadter before you read the book. Good Luck!"

Douglas Hofstadter is best know as the author of Godel, Escher, Bach: An eternal golden braid. A kind of pop-AI, maths and philosophy book which I was first encouraged to read by a Maths teacher in sixth form but which I only actually finished a couple of years ago. It's a good, if fairly dense, book and I'm not sure how comprehensible it actually is to someone who doesn't already have an AI/Maths/Phil background.

Inside the front cover is attached a letter to Hofstadter which rambles a bit and says things like "The text can be incorporated into both the Jewish and Christian tradition, but doing so with too much vigour would be to narrow its scope."

The back cover blurb implies the contents are a Swedish translation of Conan Doyle's lost "The Giant Rat of Sumatra" and adds that it is "oddly intertwined" with Hofstadter and his new book "I am a strange loop"... "which will soon be released by your Publishing House"

The Preface starts "One day I found a book. It was lying open, visible to all, but I was the only one curious enough to pick it up. This I have regretted many times." and ends "Brace yourself and turn the pages gently as you embark on a strange journey through time and space."

The contents appears to be short random pieces e.g. (page 6)

"Dedication

In commemoration of Joseph Knecht, magister Ludi Josephus III,
who abandoned `the glass bead game,'
the most beautiful of ideas,
FOR LIFE...
... UNTO DEATH"


(That's it for page 6).

Note reappearance of good old Joe K.

-

Beyond noting this is the sort of thing Who authors Lawrence Miles or Jim Mortimore might write, I'd say this was a publicity stunt for Hofstadter's new book except that it seems a pretty expensive way to do publicity - randomly posting books from Sweden with hand written addresses to vaguely related academics. It's not like I know Hofstadter in any way even though I do work in his general area.

Thoughts?
purplecat: Hand Drawn picture of a Toy Cat (aisb)
Luciano Floridi gave two invited talks at the AISB convention. The first was a two-handed public lecture with Aaron Sloman. Aaron's talk was broadly similar to his recent Thinking about Mathematics and Science lecture at Liverpool. The second was an invited talk for the academics at the conference but Floridi treated them as two halves of the same thing.

Floridi is a primarily a philosopher. His interest, as I understood it, is in understanding philosophically what is happening at the moment in the interaction between humans and computational systems, in particular with a hope that this will allow us to avoid pitfalls down the road. He made a number of interesting points which I'm going to cover in no particular order:


  • We are on the edge of a shift in how we view ourselves; "The fourth revoluation". Once we thought we were the centre of the universe but then we had to change that self perception (The Copernican Revolution). Then we thought we were uniquely created and had to change that (The Darwinian Revolution). Then we viewed ourselves as entirely rational and explicable organisms (Freud put a stop to that one). I wasn't entirely clear exactly what change in self-perception the fourth revolution was but I think it involved challenging our perception of ourselves as discrete physical objects in favour of one that viewed ourselves as interconnected informational objects. There was a surprisingly vehement negative response to this idea in much of the room (though that response was linked to my next point) which suggested that, at the very least, the concept does challenge people's perception of self in some way.

  • We are a long way from producing intelligent programs but we already have a lot of dumb but smart systems. For instance Neopets are very basic but nevertheless clearly fill an emotional need for a lot of people. Floridi posited an upsurge of dumb programs designed to mimic human companionship in very specific ways - some of these would be for entertainment only (like Neopets) but some would have more specific assistive functions (e.g., monitoring of the elderly). None would be anything like intelligent. At lot of discussion followed on whether people would be "fooled" by this. Further discussion followed that people wouldn't be "fooled" - they'd be quite aware of the limitations of such companions - but they would use them and become attached to them anyway just as they do to pets or, perhaps more relevantly, sentimental objects.

  • The Ancient Greeks had an animist view of the world in which all objects had, to some extent, a personality. With the advent of pervasive systems and RFID tags making it practical to embed limited interactivity into everyday objects we might well be cyclicly entering a view of the world in which objects once more have personality (or at least a form of interactivity). Right now its only cars that talk back to us (and only if we have GPS installed).

  • At the moment most of us view the online/informational world as, in some sense, separate from the real or physical world. As pervasive systems become more widespread this concept of separation will fade and we will less and less compartmentalise what we are doing as either an informational act (working at a computer) or a physical act (not working at a computer).

purplecat: Hand Drawn picture of a Toy Cat (aisb)
Vincent Wiegel presented joint work with Jan van den Berg investigating a criticism of a philosophical standpoint called act utilitarianism (contrasted to rule utilitarianism).

Roughly speaking, an act utilitarian evaluates each action, as they occur, in order to decide the utility of acting while a rule utilitarian acts according to a general rule about the utility. The thought experiment used to debunk act utilitarianism was that of an election. In a population of 100 an act utilitarian only votes if they are the 51st person to vote for their preferred candidate in all other situations they gain more utility by going and doing something else more interesting. Wiegel and van den Berg simulated this situation computationally. Obviously first they had some issues about why an act utilitarian might conclude they get utility only by being the 51st person to vote and of course, how they might determine that they have the deciding vote. Interestingly, when they varied their assumptions a bit so that act utilitarians only voted if they had reason to believe they were in the range of the 46th - 56th voter (or similar) - i.e., that their vote was likely to decisive then they did very well frequently getting the outcome they wished in an election while getting to do other more interesting things when the outcome was essentially a foregone conclusion anyway.
purplecat: Hand Drawn picture of a Toy Cat (ai)
I spent two hours this afternoon when I really should have been writing either the TPHOLs or ProMAS papers listening to Aaron Sloman talk in the "Thinking about Mathematics and Science" seminar series. Aaron apologised in advance that his thoughts were not well organised but the topic had turned out to be rather larger than he had at first thought.

Aaron was interested in the way that mathematics (or reasoning in general) was neither an impirical nor a completely trivial process and how we learned to reason and how that might impact on the design of intelligent systems. One of his earlier remarks was that, when studying philosophy at Oxford, he had been taught the Humean/Russellian approach to the philosophy of mathematics - essentially that mathematics is unrelated to the real world and is about the manipulation of symbol systems. He had later discovered, and agreed with, Kant's approach that Mathematics is about some other kind of non-impirical knowledge. I never studied Kant and did not even know he had written about mathematical philosophy which shows that this attitude still survived when I was studying mathematics and philosophy I would guess 20 years after Aaron did. I was a little dubious about some of this, I accept that when learning and studying mathematics we do acquire knowledge but I'm not convinced this knowledge is non-trivial (as in it doesn't follow logically from things already known) I think we are inclined to forget there are distinct resource-bounds on reasoning, both in humans and computers, which means it takes time to discover the logical consequences of known facts. However, I'm also thinking I should try and find a text book on Kant's approach to the philosophy of mathematics.

Aaron used, as examples, a number of spatial and geometrical reasoning problems. These are problems which are generally extremely simple when thought about the right way, but become tortuous if reduced to mathematical logic. His argument was that logic could not be the underlying process of mathematics. He was later picked up on this when an audience member pointed out that all computations on von Neumann machines are underpinned by Logic, so logic was the representation if such machines did spatial reasoning. I thought the obvious answer here was that although logic might by the underlying representation you were doomed if you attempted to search for the solution at the logic level and you need the more diagrammatic representation to make the reasoning problem tractable. So while logic may form an underlying representation into which all these problems can be embedded its not necessarily the language in which we, or computers, can or should reason about them, at least not if we wish to reason efficiently. My former PhD supervisor, Alan Bundy, has become extremely keen, in recent years, on the idea that the significant task in approaching a mathematical problem is to find the right representation of the problem, not the actual search for a solution. Aaron instead argued that you could not treat von Neumann or Turing machines as logical since they were embedded in the real world. Alan has also done some interesting work (I think anyway) on the way reasoning works with these representations and how this can account for some common mistakes, and some classic non-theorems.

I had not known that when he first moved into Computer Science, Aaron had worked in Computer Vision but he made the interesting point here that he felt that the computer vision people were still making the representation mistake. Seeking to interpret visual signals in order to form a precise model of the world complete with exact angles and so forth, rather than an appropriate representation for problem solving.

Niggles about logic and representation aside, it was a stimulating talk and Aaron easily held our attention for an hour and a half, followed by half an hour of questions, which is no mean feat in itself.

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