Fry’s Hello World

Hannah Fry Hello World: How to be Human in the Age of the Machine Penguin 2018

This is a popular mathematician’s take on the potential and actual impact of the rising use of algorithms on our current and possible future worlds. It is a good read. As a mathematician, though, what comes across is the author’s humanity rather than any application of mathematics. The book is not ‘about’ mathematics as such and nor does it apply mathematics to its subject. The only significance for mathematics that I can see is that it amply demonstrates that – contrary to what some people seem to think – being a mathematician does not commit you to a particular view of the uses (and abuses) of mathematics, and is entirely compatible with being human and sensible.

An ‘algorithm’ is defined as:

A step-by-step procedure for solving a problem or accomplishing some end especially by a computer.

It seems to me that much of the discussion would apply to any definite method in the sense of Turing, where the key characteristic is that each step is intended to be relatively objective, not requiring any external judgement. Thus ‘go to local store and buy something for lunch’ is not the kind of procedure that is in mind. It would be more like ‘take a definite shopping list to two stores, compare prices, buy from whichever store is cheapest, bring them home’. The conclusion seems to be that we often need to mix definite procedures with judgements, as when the stores don’t have all the items, so some judgement is needed as to what else to buy to make an acceptable lunch. From a mathematical perspective how the algorithm is implemented seems less relevant.

As an aside, Turing’s definite methods assume that each step is repeatable, but in practice we sometimes need to allow steps that include a random contribution, albeit one which is generated subject to some definite probabilistic model. This is used in all kinds of computer algorithmic forecasting, which can have huge impact on our lives (e.g., climate, economic) but is beyond the scope of this book.

Conclusion

The Magic Test

Whenever you see a story about an algorithm, see if you can swap out any of the buzzwords … and swap in the word ‘magic’. … Is any of the meaning lost? If not … something smells quite a lot like bullshit.

This seems too good a rule of thumb to relegate to a footnote, and much more widely applicable than the scope of this book. I would worry, though, that many in the intended audience would see various uses and abuses of mathematics equally as ‘magic’.

Roles

Imagine that, rather than … focussing … on … some impossible standard of fairness .. we … build algorithms to be contestable from the ground up … to support humans in their decisions, rather than instruct them … to be transparent … rather than just inform us of the result.

Again, this seems a good idea for any decision aid, not just ‘algorithms’.

Main Body

Justice

Ask the audience

[Decision] trees of the kind we made in school start to fall down. …

And yet … In what is known as an ensemble, you first build thousands of smaller trees from random subsections of the data. … The trees may not all agree, and on their own they may trill make weak predictions, but just by taking the average of their answers, you can dramatically improve the precision of their predictions.

This provides some key insights, but I have some quibbles:

  • This could do with an explicit reference, e.g. to Wikipedia. The book has many footnotes and references. Why not here?
  • I am not sure that the target audience would always interpret ‘subsections’ appropriately without further hints.
  • There seems to me to be an important broad point to be made, which is lost.

Machine Bias

Unless the fraction of people who commit crimes is the same in every group of defendants, it is mathematically impossible to create a test which is equally accurate at prediction across the board and makes false positive and negative mistakes at the same rate for every group of defendants.

But

analysis indicates how easily algorithms can perpetuate the inequalities of the past. … Any [organisation] analysing people’s data has a moral responsibility … to come clean about its flaws and pitfalls.

There are also options … the algorithm could present an opportunity to [dig deeper]: Do they have access to suitable transport … childcare? Are there societal imbalances that the algorithm could be programmed to alleviate rather than perpetuate.

Difficult decisions

   It’s the competition between intuition and considered thought that is key …. . Psychologists generally agree that we have two ways of thinking: System 1 is automatic but prone to mistakes … System 2 is slow, analytic, but often quite lazy.

Weber’s Law states that the smallest change in a stimulus that can be perceived … is proportional to the initial stimulus.

The problem in the context of justice is that Weber’s Law influences the sentence lengths … . Gaps between sentences get bigger as the penalties get more severe.

Hannah here raises some important issues, but I take a different view.

Medicine

One team recently trained an algorithm to distinguish between photos of wolves and pet huskies. … Shortly after … a professor of mathematics … told me about a conversation … [He had] passed a husky [with his four-year old] grandson [who] remarked that the dog ‘looked like a wolf’. When … asked how he knew that he wasn’t a wolf, he replied, ‘Because it’s on a lead’.

I’m not sure what we expected to take from this tale, but there seems more to it than necessarily meets the eye.

Cars

The great Church of the Reverend Bayes

It’s no exaggeration to say that Bayes’ theorem is one of the most influential ideas in history. Among scientists, machine-learning and statisticians, it commands almost cultish enthusiasm.

Bayes’ theorem … offers a systematic way to update your belief in a hypothesis on the basis of th evidence.

‘Bayes runs counter to the deeply held conviction that modern science requires objectivity and precision.’ …Bayes allows you to draw sensible conclusions from sketchy observations, from messy, incomplete and erroneous data.

Bayes is a powerful tool for distilling and understanding what we really know.

It was algorithms based on Bayesian ideas that helped solve the other questions the car [in a competition] needed to answer: ‘What’s around me?’ and ‘What should I do?’

Ironies of automation

Build a machine to improve human performance … and it will lead – ironically – to a reduction in human ability.

[Why]not flip the equation on its head and aim for a self-driving system that supports the driver rather than the other way around? A safety net, like ABS or traction control, that can patiently monitor the road and stay alert for a danger the driver has missed. Not so much a chauffeur as a guardian.

My Comments

Applied Mathematics

One way to summarise is the book is this:

Improving the solution to bad formulation of a problem can make things worse.

For example:

Improving a solution to even a formulation of a problem that is in some sense is technically correct (or even ‘true’) can make things worse if those acting on the solution misunderstand either the problem or the solution.

This has long been, and still is, a common problem for a mathematicians: At best, mathematicians as such can only ever solve technical problems with conceptions, theories and models. They can lead or at least render vital assistance to:

  1. Identify and perhaps reduce or remove any logical rough edges.
  2. Identify better questions to be asked.
  3. Solve appropriately posed previously unsolved and perhaps otherwise insoluble problems.
  4. Offer alternative methods and even approaches to solutions, which may yield benefits direct or indirect, such as increase insight.
  5. Render more efficient or otherwise practical an existing solution approach.

My view is that this is a rough order of importance, even though outside academia most mathematicians spend most of their time on the last two, which are seen as yielding identifiable benefits, whereas the first three often have unexpected or unwelcome impacts. (For example, attention to mathematical critiques of mainstream neo liberal economics have been unwelcome, since it is has been feared that they could undermine confidence in the economy.)

Fry seems largely to focus on the last two aspects. While she does present a worthwhile critique of some key misconceptions she appears to do so from a common-sense point of view rather than a mathematical one. I had hoped for more.

Therefore it is by no means an idle game if we become practiced in analysing long-held commonplace concepts and showing the circumstances on which their justification and usefulness depend, and how they have grown up, individually, out of the givens of experience. Thus their excessive authority will be broken. They will be removed if they cannot be properly legitimated, corrected if their correlation with given things be far too superfluous, or replaced if a new system can be established that we prefer for whatever reason. (Einstein)

It seems to me that mathematics, rightly, is highly regarded in this sense. Fry rightly challenges what seems to be a common view: that just because an algorithm is ‘mathematical’ in the computational sense doesn’t mean that it has been subject to mathematical analysis in the above sense. There may be some truth in Einstein’s:

Our entire much-praised technological progress, and civilization generally, could be compared to an axe in the hand of a pathological criminal.

Bayesianism

Hannah’s account of ‘the cult’ of Bayesianism rightly raises issues of my first two types, but provides no answers. Einstein remarked:

In so far as theories of mathematics speak about reality, they are not certain, and in so far as they are certain, they do not speak about reality. (1921)

The key problem, then is that if Bayesianism (or anything else) claims to be a theory about reality, it must be uncertain, and hence can’t be trusted. Einstein is here following the then current American usage. I would rather follow Whitehead et al in saying that mathematics as such is silent about reality: that would be the province of physics. But a notable feature of Bayesianism is that its advocates justify by reference to mathematics, and many mathematicians seem to think it justified by reference to physics. This may satisfy the many, of whom Einstein said:

Many take to science out of a joyful sense of superior intellectual power; science is their own special sport to which they look for vivid experience and the satisfaction of ambition; many others are to be found in the temple who have offered the products of their brains on this altar for purely utilitarian purposes.

But there is surely more to be said if we are to live up to Einstein’s assessment:

One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.

Summary

What we might benefit from is some mathematics to add power to Hannah’s ‘Magic test’. The views that I quibble with above might be a good place to apply such tests. We might then work towards Fry’s concept of a decision aid, that supports us in our activity, scanning the horizon and altering us to potential danger.

Related Work

  • Finkelstein’s idea of the  pre-mortem, as supporting the ‘call to arms’.

To be continued (it’s sunny out!)

 

Dave Marsay

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