How We Know What We Know: Introduction

I’ve been reading up a lot over the last few years about a large variety of subjects, not science as such but how we do science and how we actually know what we know. I’ve written about some of these things before, in Sci-Ence! Justice Leak!, but there I was looking at stuff for its science-fictional or storytelling possibilities.

However, I want to write about this stuff seriously. Partly, that’s to help organise my own thoughts – I’m an autodidact, and I’ve read a VAST amount without trying to organise it except in an ad hoc manner. But also, it’s because I find this stuff absolutely fascinating. So I’ve come up with a through-line, and I’m going to try to do a post a week for the next twelve weeks. I’m going to try to be properly accurate, but still convert this all into vernacular English.

What I’m going to talk about is the scientific method – what it is, why it’s important, and how developments in computer science have meant we can create and prove, based on a very small set of assumptions, a mathematically rigorous formulation of the scientific method. Not only that, but we can use that prove what the optimal thing to do is in all circumstances (given enough computing power…)

There will be twelve parts to this series:

1 – Feedback
Explaining possibly the most important concept in human thought, and looking at the hypothesise-experiment-revise process in science.

2 – Occam’s Razor
The single most important tool in modern science, invented by a mediaeval monk.

3 – Proof By Contradiction
A mathematical technique, first formulated by Euclid, that’s the basis for much modern mathematics.

4 – Diagonal Proof
Georg Cantor’s proof and why it’s important

5 – Turing and Godel
On notions of computability, and what a computer program is.

6 – Kolmogrov Complexity
What’s the smallest computer program that could print out this essay?

7 – Bayes’ Theorem
An 18th century vicar shows us how to make decisions in the absence of information.

8 – Ashby’s Law
Cybernetics and attempting to control the uncontrollable

9 – Thermodynamics and Shannon
What is information, and how is it related to chaos?

10 – Solomonoff Induction
How to predict the future

11 – Hutter’s algorithm
Universal artificial intelligence

In which we look at what we’ve learned.

This will be summarising stuff from many books and articles, but in particular The Fabric Of Reality by David Deutsch, Probability Theory — The Logic Of Science by E.T. Jaynes, Information Theory, Inference, and Learning Algorithms by David MacKay, some of the posts on the LessWrong group blog, the lectures in Scott Aaronson’s sidebar and An Introduction To Cybernetics by W. Ross Ashby. Mistakes are, of course, mine, not theirs. Part 1 in this series will come next week.

(More generally my plan at the moment is to have four big series of posts on the go – my Beach Boys reviews, starting up my Doctor Who reviews again, this series and a series of posts on Cerebus – all posting roughly weekly, with the other three days of the week left either for linkblogs or for rants on whatever comes to mind in comics or politics).

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7 Responses to How We Know What We Know: Introduction

  1. FrF says:

    Inspired by, I’m making my way through Cerebus and I’m very impressed by the artist (Dave Sim) as a young man. As early as issues 11 (“The Merchant & The Cockroach”) and 13 (“Black Magiking”) Sim was “firing on all cylinders”. Now I’m reading the Palnu trilogy but I’m advancing only slowly because Sim’s artwork is such a joy to take an interrupting-the-narrative-flow look at.

    And I certainly won’t miss your scientific method series!

    • Andrew Hickey says:

      He only gets better – especially when Gerhard comes on on backgrounds. You’ll be amazed.

      • FrF says:

        Oh, I know large parts of the “High Society/Church And State/Jaka’s Story” axis. I was surprised how early the series got really good. I didn’t even own the first phonebook (which according to Cerebus Wiki is the bestselling installment of the book collections).

        I’m also thankful for CerebusTV. For me it serves as a welcome reminder to a more well-rounded picture of Dave Sim. He doesn’t necessarily have to be defined by the quirks of his weltanschauung. Of course, whenever I become too unwary, along comes another round of Glamourpuss’ fashion magazine parodies!

  2. Zom says:

    There’s an excellent Philosophy talk podcast about how we evaluate and sift information. One of the most interesting topics discussed was how we often (possibly normally) judgements based on insufficient factual information. The expert on the panel didn’t see this as necessarily a bad thing, just a brute fact of the human condition. In his view the issue is around our ability to discrimate between poor received information and argumentation and its opposite.

    Not exactly what you’re talking about, but in the arena of epistemology nonetheless

    • Andrew Hickey says:

      That is actually quite close to some of this stuff – I’m going to be talking a lot about how we make judgements given uncertainty. Surprisingly, with the right tools, having bad information doesn’t necessarily get you bad results.

  3. Zom says:

    I suspect in a lot of instances it has to do with the ability to evaluate evidence, assess it’s reliability and suchlike, and take action/form opinions based on the evaluation rather than simply the information itself.

    Mind you, one of the reasons why I loathe Rupert Murdoch’s influence is that it pretty much guarantees vast swathes of bad information, and given that a lot of people are bad at evaluating the kinds of bad information he puts out that can only be A Bad Thing.

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