Category: Logic

Is Hidden Figures Science Fiction?

I’ve actually written a longer piece on this film, which is still unfinished and may be unrescuable because of far too many tangents (less obvious ones including Aleksandr Solzhenitsyn, Alfred Hitchcock’s use of a toilet, and the nasty rightwing Christian ‘Focus on the Family’ group). In the meantime, this is an attempt to address the question I intended to address in the other piece but never actually reached. Somehow Ludwig Wittengstein* ended up in this one. Sorry, he gets everywhere.

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Farewell Raymond Smullyan

Martin Gardner was a kind of gateway drug. When I was a kid I went to the same secondary school that my dad taught at. That wasn’t a particular problem for me but it meant I had to hand around school until he was heading home.

This meant sitting in the school library by myself reading, which, being a bookish sort, was not any great hardship. I ploughed through the sci-fi books but on other occasions, I’d just look at random books.  It was in this way I stumbled across old Penguin (or Pelican?) editions of Gardner’s Mathematical Puzzle’s and Diversions books. Now, I was not much of one for mathematics at the time but I liked puzzles and I liked the odd, arcane nature of these books.

As an older teen Gardner led me to other writers: Douglas Hofstadter (notably I read Metamagical Themas first then Godel, Escher, Bach) but also Raymond Smullyan.

Like Gardner, Smullyan combined a love of puzzles and magic but also the absurd. That logic and absurdity are natural companions is something that people find paradoxical. People think it odd that Lewis Carroll was both an eminent logician and author of Alice in Wonderland despite the absurdism of the Alice books often relying on wordplay and uncooperative literalism.

Smullyan, who died last Monday (Feb 6th 2017) tied absurdity more closely to logic in his complex puzzle books. The connection is overt – using weird settings and strange kinds of people (knights, vampires among others) with proscriptive approaches to communication. The New York times has a substantial sample here https://www.nytimes.com/interactive/2017/02/11/obituaries/smullyan-logic-puzzles.html

So why the close connection between the absurd and logic?

Two elements are at play. Firstly the necessary insistence on literalism. Exactly WHAT is being said? It is an insistence that when applied to normal conversation is a breach of normal social conventions. Secondly, the use of absurd or nonsensical propositions and conclusions helps highlight FORMAL aspects of an argument from informal and empirical aspects. To see how a syllogism functions (for example) it can be misleading to use a string of commonplace truths.

For example, Wikipedia uses this example for Felapton:

No flowers are animals.  All flowers are plants. ∴ Some plants are not animals. (SoP)

But to see the formal connection writers like Carroll might use more odd juxtapositions

No elephants are professors.  All elephants are stamp collectors.  ∴ Some stamp collectors are not professors.

Formal truths need to hold even in absurd worlds.

Smullyan wrote a whole bunch of wonderfully weird books, that used puzzles and odd juxtapositions to exemplify logic and reasoning. I think his most substantial achievement was Forever Undecided: A Puzzle Guide to Godel that used his signature style to lead the reader to Godel’s incompleteness theorems in a charmingly accessible manner.

Logician, Taoist, Magician – a 97 year life of tricks, puzzles and deep thoughts.

 

Meat Robot 1: Free Will

John C Wright started an interesting discussion at his blog http://www.scifiwright.com/2016/08/a-general-query-to-all-panphysicalists-and-radical-materialists/

Let us cut to the chase.

Think back to the day when you first discovered that you were a meat robot without free will, without freedom, and without dignity. Did the discovery fill you with awe, rapture, wonder and gratitude?

For, if not, the discovery is false. Truth is majestic and majesty provokes awe; truth is sublimely beautiful and beauty provokes rapture; truth is startling, because it shatters the lies we tell ourselves, and the bright surprise leaves us blinking in wonder; truth is a gift to be prized above all price, and gifts provoke gratitude.

If the discovery of material did none of these things, either your reactions are miscalibrated and do not reflect reality, or your discovery was not a discovery at all, merely a falsehoods you have yet to test with due rigor.

So? What was your reaction?

There were two more posts and the discussion above was a follow on from previous discussions.

I hadn’t been commenting at JCW’s blog because it tended to cause more upset than discussion but this post looked like an invitation back. As it happens, things started to get weird and tense there and I opted out again. However, there were some intelligent questions asked and I said I’d try and address them.

And fair warning: this goes on a bit and involes some thought experiments about predicting other people’s behaviour which is neccesarily a bit creepy-when-you-think-about-it sort of philsophical scenario.

Free Will

I’m not going to cite anybody in this chunk but the ideas below aren’t original.

Free will is conceptually a mess but it is also something people grasp as a thing they experience. When I say it is a mess, what I mean is:

  • If you are Judeo-Christian-Islamic theist then you have to reconcile free-will with a god that can do anything and knows everything in advance.
  • If you believe in any kind of determinism (physical or theological) then you have to somehow reconcile that with the supposed choices of free-will.
  • If you believe the world is more unpredictable then you escape determinism but swap forced choices for random ones.

Free will is cognitive: it is about a person making free choices and deciding to do something. While that can encompass spontaneity or seemingly random acts, it isn’t confined to such acts. We would regard our rational and/or sensible choices to also be encompassed by free-will.

Also, we tend to see as our choices defining us – they are the kinds of things we would do. Our choices reflect our personality and our history. We can also reflect on our decision making and consider how the information we had, our emotional state, our personal goals and our personality influenced our decision.

Wright sees free-will as being particularly challenged by a physical view of reality. If I am a robot made of meat (I am – but one running a Camestros Felapton module) then I am like a clockwork machine and my thought processes are reducible to atoms moving about and hence no free-will. I’ll put aside, for the time being, the question of things being usefully reducible to physics

I’ll put aside, for the time being, the question of things being usefully reducible to physics. At a broader level, my mind is the operations of my brain and my brain operates at levels some of which I’m not conscious of. This can be alarming because it begins to sound like my brain is in charge of me rather than my mind.

Neurologically there is apparent evidence for this, with some indication of things occurring in the brain pertaining to decisions before we are conscious of having made our decision.

I think this is actually unremarkable. Whether we imagine souls, gods, quantum effects creating intelligence or computer-like brains, an unconscious process will precede conscious ones. To imagine otherwise is to assert our thought processes transcend time and that is a point where I resort to saying that is just silly.

The problem is we really don’t have a good handle on what free-will is. As a consequence, we tie ourselves into paradoxes. So I’m going to assert what free-will is – again this is not original with me but I don’t have a pointer to a specific thinker who said this.

What Free Will Is

Imagine a person, call her Sue.

We have the power to predict what Sue will do. How have we got that power? You can pick the way you feel most comfortable with:

  • Access to a parallel universe which is temporally further ahead than ours but otherwise the same (currently).
  • An extraordinary computer simulation of Sue that tracks all inputs and physical states of Sue to produce a deterministic model of Sue that predicts exactly what she will do.
  • An angel tells us what decisions Sue will make.
  • All of these choices are actually a bit disturbing when you think about it and you’d rather not pick any of them, thanks very much.

It doesn’t matter which we pick. Somehow, we can know what Sue will do next.

I believe Sue can still have free-will in this scenario.

That is important. I’m not saying she must have free-will, it could still be a contingent fact about our universe that free-will is an illusion but even with the kind of determinism I just described, I think free-will is still possible. Having said that, we need to describe it carefully.

We meet Sue for a cup of coffee. Our predestination powers tell us that Sue will order a cappuccino. Note how unremarkable a prediction this is. It is the kind we make fairly reliably about people we know, despite not having any remarkable powers. However:

  • Sue does not know about our power to see what she will do next.
  • We have not told Sue that we know she will order a cappuccino.

Sue orders a cappuccino.

Over coffee, we explain to Sue that we have this incredible power to predict her decisions. Sue is naturally aghast at this gross invasion of her privacy, demands that we smash up the computer/stop accessing a parallel universe/stop talking to messed-up angels. Still, the idea gets stuck in Sue’s head and she decides to teach us a lesson.

She uses what we told her to build her own simulation/access a parallel universe/contact an angel and now has he power to see what WE will do next.

She asks to meet us for a cup of coffee. Before we order, Sue explains what she has done and also that she knows we will order a cup of tea. Because we are somewhat infantile and cross that Sue has neatly demonstrated how messed-up it would be to gain pre-knowledge of another persons actions, we rather petuantly decide to order a cappuccino.

  • We order a cappuccino.

That is free will.

Sue asks us to check our Sue-predicting-powers and we discover that:

  • Our parallel universe Sue is now an alt-history Sue and the universe is slightly different.
  • Our computer model has diverged from Sue’s behaviour.
  • The angle is lecturing us on how god works in mysterious ways.

Of those options, the only one I can actually garuntee is the computer one. Sue’s model of us and our model of Sue must contain everything Sue knows and believes about the world. Whether that is at fundamental level of how the data is encoded in neuron’s or pulses of electrons or arrangements of atoms or whether it is at a more comprehensible level, it doesn’t matter. All of us make decisions based on what we know and believe and have been told.

Sue predicted that we would order tea but that prediction did not contain the fact that she would tell us about the prediction. Our mental state is changed by Sue telling us about the prediction (which we believe because of our past experience with such predictions).

Sue could have anticipated this and fed back into the model of us that she would tell us about ordering tea. In that case her computer model then has to take into account its own predictions. Maybe it collapses into a self-reference paradox at that point or maybe it copes and says that I’ll order a cappucinno…but then Sue has to tell me I’ll order a capuccino…so I order tea…so Sue would need to feed in double, triple, quadruple layers of prediction. Even numbered predictions would be cappuccino and odd numbered would be tea.

This isn’t just an exercise in the logic of determinism. Socially and evolutionarily, other people need our behaviour to be predictable (it is how we all get along) and we need our behaviour to have the capacity to be surprising (it’s what stops people taking each other for granted).

Even at a very fallible level of predicting another person’s behaviour, we know that telling somebody what choice they will make in advance is at best cheeky and more generally is rude. The scenario above of some supposedly infallible predictor of a person’s behaviour is worse than rude but would be downright creepy, weird and unethical.

Meat robot is quite happy thanks

As a meat robot I’m confident I have free-will. My decisions are determined in the sense that the component parts of me together make up ME and it is the interaction of those parts on what I know and believe about the world that make up my decisions. That isn’t a loss of free-will, it is just being honest about who and what I am. I’m not an abstract geometrical point or a monad. I’ve got parts.

Within that framework, I can make sense of what it means for me to have free-will. Not only that, free-will makes sense LOGICALLY and also EVOLUTIONARILY.

  • Logically because a deterministic prediction of what I will do is still something I can defy because such a prediction to be foolproof would require the capacity to model its own predictions in the event of me learning about its predictions. Heck, even decsribing the issue gets you into a self-referential nest.
  • Evolutionarily because meat-robots are social animals and that requires us to be both predictable and surprising.

I’m not saying divine or metaphysical explanations of free-will are neccesarily wrong (although they have issues and I’ll touch on some of them in other posts) but I am saying free-will makes a lot of sense for a meat robot.

Discovervented – the ultimate speculative fiction

piflagThis a belated American Pi Day post. I say ‘American Pi’ day not for an opportunity to make Don Mclean puns but because March 14 only looks pi-like if you do the month/date thing. Elsewhere it was 14/3, which could be 1.43 day or less-good-square-root-of-2 day (Feb 14 being better but Dec 14 being best). For the day/month people July 22 makes a better Pi day as it gives the classic rational approximation of 22/7.

I was asked where I stood on the issue of Pi being invented or discovered. I’m firmly in the discovervented camp.

The ‘discover’ camp tends towards Platonism – the idea that mathematics is not just real but really real. Indeed mathematics in Platonism is more real than reality, which is just a crappy shadow of truth, goodness and all things geometrical. Discovered feels right but if you follow the reasoning you end up having to swallow a very big metaphysical pill.

The ‘invented’ camp tends towards Formalism – the idea that mathematics is the logical outcomes of arbitrarily chosen rules. I’m much more inclined towards formalism but it can feel a bit arbitrary. After all we could make up all sorts of self-consistent logical schemes and prove empty theorems about them but we don’t. The ones we study in mathematics not only tend to be relevant ones but have had an uncanny knack of BECOMING relevant.

Aristotle pitched his tent just a little way away from Plato. From him mathematics was something embedded in the universe but maybe not as transcendental as Plato took it to be.
From Kant and modern notions of evolution and modern psychology and neuroscience we get an alternate notion of embedding – that mathematics is something kind of built into us and the way we make sense of the universe.

I’ll play pick and mix with all that. I do tend towards FICTIONALISM as a model of mathematical truth, which marries nicely with formalism. That is a mathematical truth like 2+3=5 is true in a similar sense as ‘Sherlock Holmes lived at 221b Baker Street’. Mathematics is a kind of fiction, a work of imagination but as any writer knows your imagination is constrained by your experience and by your contact with reality and by what makes sense and by what is self-consistent.

Mathematics is like that as well. We invent it to describe the world around us but in doing so we create a space which we explore within rules and then discover things. If we invent the abstract notion of a ‘circle’ based on our real world experiences of circles and a concept of ‘diameter’ and ‘circumference’ then we discover in our inventions a little pi, like an alchemic homunculus. Which is all well a good but then we find the same little fellow starting out at us in our other inventions and we begin to suspect Plato was right all along.

But if mathematics is fiction, what kind of fiction is it? Well in modern times we associate it with science but in the past it has played nicely with mystical and religious disciplines as well. Mathematics is like some strange kind of genre, a genre that can encompass imaginary realities, alternative sciences but also magic and fantastical worlds all within a broader notion of the weird and the speculative. Mathematics is the ultimate SF/F.

Is Martin Freeman Lucy Liu? (and other theological questions)

CumberLiu In the US a Christian college is sanctioning a member of its staff who asserted that Islam worships the same god as Christianity. Apparently this is a controversial notion and at odds with the college’s official doctrine. Now for an atheist the argument is a bit like asking whether Benedict Cumberbatch and Johnny lee-Miller both play the character called Sherlock Holmes on television. Now that is a really fun argument to have but not one likely to get you sacked from your job if you take the wrong position. However, for people who are followers of the so-called Abrahamic religions this can be an important question.

Interestingly, it is a debate that is burning away over at Vox Day’s blog

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