Spoiler-Free Review of Jurassic World: The Fallen Kingdom

Jurassic World: The Fallen Kingdom is the latest addition to the Jurassic Park/Jurassic World franchise, and strikes an uneasy balance between retreading old themes and covering new material.  There are the dinosaurs; there are the heroes and the villians; there's even a child cowering and quaking while a dinosaur approaches.  It's all there - if you've seen and enjoyed the previous films, you'll enjoy this one too.

Universal Pictures

The story moves at a very good pace - yes, there are the slower, plot-development scenes where the villains outline their master plan, and the heroes trade jokes and contemplate the future of dinosaur-kind.  I won't share too much of the plot, but Owen and Claire are persuaded to return to Isla Nubar when it's discovered that it's an active volcano and all the dinosaurs are going to be killed.  The return to the island is filmed particularly well, as we see a Jurassic World that has fallen into disrepair, death and decay, in stark contrast to the lavish bright colours we saw in the previous film.  The aftermath of the Indominus's rampage is visible everywhere (including in some very neat detail shots).

The visual effects of dinosaurs plus volcano are extremely well executed, and there is the usual quota of running, shouting, chasing, and hiding, all delivered at breakneck speed. In fact, it's so fast that you may miss one or two of the plot developments, but fear not, there's plenty of chance to catch up.  The entire second half of the film takes place off the island - so this is unlike most of the previous films.  Yes, there are comparisons with The Lost World, but this film has a lot more about it than that.

Is the film scary?  Yes.  There are plenty of suspenseful moments... teeth and claws appearing slowly out of the murky darkness; rustling trees getting closer - all that stuff.  This is more scary than the high-speed dinosaur vs human or dinosaur vs dinosaur stuff - and there's plenty of that too.  There are two extended scenes in the second half where one particularly nasty dinosaur starts stalking its human prey, but apart from that there's not much that we haven't seen before.

Is it gory?  No.  Despite a body count that puts it on a par with the other films, there isn't much visible blood - one character has his arm bitten off, and the amount of blood is almost too small to be plausible.  There's at least one death on camera, but it's out-of-focus and in the background.  I took two children - aged seven and nine - with me, and the nine-year-old was upset by some of the tragic scenes, but neither of them were particularly scared.

All-in-all, I liked this film: it is exactly what you would expect, with some interesting twists.  I know it's had mixed reviews, but it does a good job of staying true to its roots while expanding the wider storyline in a number of unexpected ways.  The speed at which the film moves through the plot, with some serious and irreversible actions, means that this is - in my view - more than just another sequel and is not as derivative as some make it seem.

Online Optimisation: Testing Sequences

As your online optimisation program grows and develops, it's likely that you'll progress from changing copy or images or colours, and start testing moving content around on the page - changing the order of the products that you show; moving content from the bottom of the page to the top; testing to see if you achieve greater engagement (more clicks; lower bounce rate; lower exit rate) and make more money (conversion; revenue per visitor).  A logical next step up from 'moving things around' is to test the sequence of elements in a list or on a page.  After all, there's no new content, no real design changes, but there's a lot of potential in changing the sequence of the existing content on the page.
Sequencing tests can look very simple, but there are a number of complexities to think about - and mathematically, the numbers get very large very quickly.  

As an example, here's the Ford UK's cars category page, www.ford.co.uk/cars.

[The page scrolls down; I've split it into two halves and shown them side-by-side].

Testing sequences can quickly become a very mathematical process:  if you have just three items in a list, then the number of recipes is six; if you have four items, then there are 24 different sequences (see combinations without repetition).  Clearly, some of these will make no sense (either logically or financially) so you can cut out some of the options, but that's still going to leave you with a large number of potential sequences.  In Ford's example here, with 20 items in the list, there are 2,432,902,008,176,640,000 different options.

Looking at Ford, there appears to be some form of sorting (default) which is generally price low-to-high and slightly by size or price, with a few miscellaneous tagged onto the end (the Ford GT, for example).  At first glance, there's very little difference between many of the cars - they look very, very similar (there's no sense of scale or of the specific features of each model).

Since there are two quintillion various ways of sequencing this list, we need to look at some 'normal' approaches, and are, of course, a number of typical ways of sorting products that customers are likely to gravitate towards - sorting by alphabetical order; sorting by price or perceived value (i.e. start with the the lower quality products and move to luxury quality), and you could also add to that sorting by most popular (drives the most clicks or sales).  Naturally, if your products have another obvious sorting option (such as size, width, length or whatever) then this could also be worth testing.

What are the answers?  As always:  plan your test concept in advance.  Are you going to use 'standard' sorting options, such as size or price, or are you going to do something based on other metrics (such as click-through-rate, revenue or page popularity)?  What are the KPIs you're going to measure?  Are you going for clicks, or revenue?  This may lead to non-standard sequences, where there's no apparent logic to the list you produce.  However, once you've decided,  the number of sequences falls from trillions to a handful, and you can start to choose the main sequences you're going to test.

For Ford, price low to high (or size large to small), popularity (sales), grouping by model size (hatchback, saloon, off-road/SUV, sports) may also work - and that leads on to sub-categorization and taxonomy, which I'll probably cover in an upcoming blog.






 

Chess and Machine Learning?

Machine learning is a new, exciting and growing area of computer science that looks at if and how computers can learn without explicitly being taught.  Within the last few weeks, machine learning programs have learned games such as Go and Chess, and become very capable players: Google's AlphaZero beat the well-known Chess engine Stockfish after just 24 hours of learning how to play; just over a year ago, AlphaGo beat the world's strongest human player Ke Jie at Go.

AlphaZero is different from all previous Chess engines, in that it learns by playing.  Having been programmed with the rules of Chess (aims of the game; how the pieces move), it played 1000 games against itself, learning as it went.  The Google Alpha Zero team have published a paper of their research, and it makes for interesting reading.

From a Chess perspective, the data is very interesting as it shows how Alpha Zero discovered some key well-known openings (the English; the Sicilian; the Ruy Lopez) and how it used them in games, and then discarded them as it found 'better' alternatives.  Table 2 on page 6 shows how the frequency of each opening varied against training time.  There are some interesting highlights in the data:

The English Opening (1. c4 e5 2. g3 d5 3. cxd5 Nf6 4. Bg2 Nxd5 5. Nf3) was a clear favourite with Alpha Zero from very early on, and grew in popularity (I played the English once).

The Queen's Gambit (1. d4 d5 2. c4 c6 Nc3 Nf6 Nf3 a6 g3 c4 a4) also became a preferred opening.

Interestingly, the Sicilian Defence (1. ... c5) was not favoured, instead the preferred line against 1. e4 was the Ruy Lopez (1 ... e5).

It's worth remembering that Alpha Zero deduced these well-known and long-played openings and variations by itself in 24 hours - compared to the decades (and centuries) of human play that has gone into developing these openings.

Apart from the purely academic exercises of building machines that can learn to play games, there are the financially lucrative applications of machine learning: product recommendations.  Amazon and Netflix make extensive use of recommenders, where machines make forecasts about a user, based on users who showed similar behaviour ("people who liked what you like also like this...").  Splitting out and segmenting all users to find users with similar properties is a key part of the machine learning process for this application.

In conclusion:  "It's an exciting time for Machine Learning.  There is ample work to be done at all levels: from the theory end to the framework end, much can be improved.  It's almost as exciting as the creation of the internet."  Ryan Dahl, inventor of Node.js

Why are manhole lids circular?

I remember reading this question - and its answer - in a maths puzzle book in my mid teens. It's a very simple solution - and very easy to start investigating further.  The short answer: manhole lids are circular so that they don't fall down the hole (risking losing the lid, and landing on a worker who is in the hole).  Technically, the lid has a constant maximum diameter irrespective of which angle you use to measure it. 

The same cannot be said of most other polygons - let's take some quick examples.

Squares: the sides are shorter than the diagonals, so a small rotation will enable the lid to fall down the hole.
Pentagons: the ratio of side to diameter is smaller, but it's still possible to drop the lid down the hole.

Equilateral triangles are an exception; and in fact you do sometimes see manhole lids that are equilateral triangles (sometimes hinged along one side).

The same principle applies to coins. In order to function correctly,  a vending machine has to be able to identify and distinguish different coins, based on their diameter and irrespective of how they fall through the slot.  The coins which are not circular are based on Reuleaux polygons, such as the Reuleaux triangle, where the shape has a constant diameter - the key requirement for coins, and manhole covers!

Some other 'everyday maths' articles I've written:

A spreadsheet solution - the nearest point to the Red Arrows' flightpath from my house
The Twelve Days of Christmas - summing triangle and square numbers
Why are manhole lids usually circular?

Film Review: Star Wars The Last Jedi

I loved it.

My first impressions from the first few minutes was that this was a retread of Empire Strikes Back.  The First Order have tracked down the resistance base on a remote planet, and the resistance are trying to evacuate before the First Order land troops and... oh, wait a minute, there is no shield, no cannon and the base is going to be obliterated from space.  And things seem to go well for the resistance, as they are able to stall long enough to get almost everybody safely aboard their cruiser and off to safety.  But not before Poe Dameron (X-Wing ace turned hot-headed insubordinate comedian pilot) decides to sacrifice the entire bomber fleet just to destroy a Dreadnaught.  Let's here it for Pyrrhic victories!

Worse still, the First Order have developed a way to track the Resistance through hyperspace: running away is not a way to escape, and hyperspace fuel is in limited supply.

At the end of the previous film, Rey had successfully tracked down Luke Skywalker, and much of this film covers her efforts to persuade him to join the Resistance.  So, we have space battles interspersed with the story of a Jedi master and a young Jedi-wannabe/trainee on a remote, green, damp planet.  Like I said, I kept recalling Empire Strikes Back throughout this film. I haven't looked online to see if anybody has listed all the parallels between The Last Jedi and The Empire Strikes back, but I saw a few (and I'm only a casual movie-goer).  Luke Skywalker has traded his youthful naivety and enthusiasm for jaded cynicism.  The way he casually lobs his lightsabre over his shoulder is both funny and tragic at the same time.

My only niggle with the film is the amount of time spent on the story with Rey and Luke.  The other storylines were far more exciting and just downright interesting; Luke and Rey - less so.  Luke goes for a walk.  Luke catches a fish.  Luke wanders around his island.  Yawn.

The plot makes a lot of sense, and there's a direct causal link between the Admiral and her tight-lipped need-to-know authoritarian attitude, conflicting with Poe Dameron's "we have a right to know what's going on" and the subsequent demise of the resistance fleet.  If she'd told Poe what her plan was, he wouldn't have sent Finn off to find the code breaker, who wouldn't have subsequently told the First Order about the resistance's plans and their cloaking frequency (or whatever it was).  If they'd all stayed home, sat tight and waited it out, they might all have survived.  I'm not blaming him or her, but it seems like the two characters managed to deliberately out-hard-head each other - aiming to be the most stubborn character and the one who wins, until neither of them do.

Some of my favourite aspects of the film is how the script addresses some of the criticisms that were levelled at the first of the new films (The Force Awakens).

"Finn should have had that fight with Captain Phasma, not with some random stormtrooper with a cool elbow mounted weapon."  Cue large-scale, violent, hand-to-hand fight between Finn and Phasma.

"Snoke is too much like the Emperor and there's no real explanation for him."  Kill him off - now who saw that coming?

"More Poe Dameron!" - definitely fixed in this episode.  He kicks off the action at the start; we see more of his character throughout this film (borderline arrogant, but still funny) and he commits mutiny.  This is not a replacement for Han Solo; this is a whole new character who has his own ideas, opinions and history.

"Do something different!"  - I saw most of the parallels between The Force Awakens and A New Hope.  In fact, it felt like a rehash of the story with new faces. As I mentioned earlier, The Last Jedi has elements of The Empire Strikes Back in it, but those elements have been rearranged to produce a fresh story (and no, I didn't for one second think "It's salt!", I knew full well it was meant to be snow).

All-in-all, I'm excited for the next installment; I'm looking forwards to the Han Solo movie and I feel even more optimistic for the future of the Star Wars saga.

Some of my other film reviews:
Cloverfield
Inception
The Green Hornet
Transformers 2: Revenge of the Fallen
Transformers 3: Dark of the Moon
Transformers: Bumblebee
Transformers: One
Tron
Wing Commander
Pixels

Mathematically Explaining Confidence and Levels of Significance

Level of Significance: a more mathematical discussion

In mathematical terms, and according to "A Dictionary of Statistical Terms, by E H C Marriott, published for the International Statistical Institute by Longman Scientific and Technical":

"Many statistical tests of hypotheses depend on the use of the probability distributions of a statistic t chosen for the purpose of the particular test. When the hypothesis is true this distribution has a known form, at least approximately, and the probability Pr(t≥ti) or Pr(t≥t0), and Pr(t ≤ ti) and Pr(t ≤ t0) are called levels of significance and are usually expressed as percentages, e.g. 5 per cent.  The actual values are, of course, arbitrary, but popular values are 5, 1 and 0.1 per cent."

In English: we assume that the probability of a particular event happening (e.g. a particular recipe persuading a customer to convert and complete a purchase) can be modelled using the Normal Distribution.  We assume that the average conversion rate (e.g. 15%) represents the recipe's typical conversion rate, and the chances of the recipe driving a higher conversion rate can be calculated using some complex but manageable maths.  

More data, more traffic and more orders gives us the ability to state our average conversion rate with greater probability.  As we obtain more data, our overall data set is less prone to skewing (being affected by one or two anomalous data points).  The 'spread' of our curve - the degree of variability - decreases; in mathematical terms, the standard deviation of our data decreases.  The standard deviation is a measure of how spread out our data is, and this takes into account how many data points we have, and how much they vary from the average.  More data generally means a lower standard deviation (and that's why we like to have more traffic to achieve confidence).

When we run a test between two recipes, we are comparing their average conversion rate (and other metrics), and how likely it is that one conversion rate is actually better than the other.  In order to achieve this, we want to look at where the two conversion rates compare on their normal distribution curves.

In the diagram above, the conversion rate for Recipe B (green) is over one standard deviation from the mean - it's closer to two standard deviations.  We can use spreadsheets or data tables (remember those?) to translate the number of standard deviations into a probability:  how likely is it that the conversion rate for Recipe B is going to be consistently higher than Recipe A.  This will give us a confidence level.  It depends on the difference between the two (Y% compared to X%) and how many standard deviations this is (how much spread there is in the two data sets, which is dependent on how many orders and visitors we've received.

Most optimisation tools will carry out the calculation on number of orders and visitors, and comparision between the two recipes as part of their in-built capabilities (it's possible to do it with a spreadsheet, but it's a bit laborious).

The fundamentals are:

- we model the performance (conversion rate) of each recipe using the normal distribution (this tells us how likely it is that the actual performance for the recipe will vary around the reported average).
- we calculate the distance between conversion rates for two recipes, and how many standard deviations there are between the two.
- we translate the number of standard deviations into a percentage probability, which is the confidence level that one recipe is actually outperforming the other.

Revisiting our original definition:Many statistical tests of hypotheses depend on the use of the probability distributions of a statistic t chosen for the purpose of the particular test

...and we typically use the Normal Distribution When the hypothesis is true this distribution has a known form, at least approximately, and the probability Pr(t≥ti) or Pr(t≥t0), and Pr(t ≤ ti) and Pr(t ≤ t0) are called levels of significance and are usually expressed as percentages, e.g. 5 per cent.

In our example, the probabilities ti and t0 are the probabilities that the test recipe outperforms the control recipe.  It equates to the proportion of the total curve which is shaded:

You can see here that almost 95% of the area under the Recipe A curve has been shaded, there is only the small amount between t1 and t0 which is not shaded (approx 5%).  Hence we can say with confidence that Recipe B is better than Recipe A.

Thus, for example, the expression "t falls above the 5 per cent level of significance" means that the observed value of t is greater than t1 where the probability of all values greater than t1 is 0.05; t1 is called the upper 5 per cent significance point, and similarly for the lower significance point t0."

As I said, most of the heavy maths lifting can be done either by the testing tool or a spreadsheet, but I hope this article has helped to clarify what confidence means mathematically, and (importantly) how it depends on the sample size (since this improves the accuracy of the overall data and reduces the standard deviation, which, in turn, enables to us to quote smaller differences with higher confidence).

New Year's Resolution - Don't moan, complain.

One of my New Year's Resolution's for 2018 is this: don't moan, complain.

What's the difference?

We're very good, as a society, at moaning. Social media has made it even easier to bend our friends' ears about the latest irritation that we've had to suffer: long queues; poor service; sub-standard goods; cold food; inept staff; rude checkout assistants... the list goes on. And we think that sharing our dreadful experience with our friends will avenge us on the service provider - we "warn" our friends against giving their money to the same company and encourage them to support their competitors instead.

That is not complaining; that's moaning.

Moaning: telling everyone about a terrible experience - except the people who (1) caused your inconvenience and/or (2) are in a position to fix your situation or provide redress.  

Complaining: approaching the person who provided the poor service; the lousy product; the long wait or the cold food, and asking them to please fix it.

I don't tend to complain - I think it's rude; I don't want to cause a scene; I don't want to be an inconvenience; I think should just tolerate it and make it a character-building opportunity.

However, I think it's time to make a change, and - when necessary  - to complain instead of biting my tongue (I'd like to think I don't moan much, but the principle is the same). Some stores, cinemas and so on ask for feedback - some shops will enter you for a prize draw if you do - which is a good place to start, but how about this: if you think you're going to go home and then tomorrow tell your friends how bad this place/shop/meal was today, why not tell the staff today? Or at least contact their complaints department so that they can actually do something about it. Make a difference, so that they can make a difference too.

My New Year's Resolutions, over the years:

My New Year's Resolutions for 2017
Spend Less Time on Trivial Matters
Give More Than I Receive
Repair, Not Replace
Produce More Than I Consume
A review of my 2017 resolutions
Don't Moan, Complain