The cool, unflappable logic of a computer may seem infinitely more intelligent than an irrational, emotional, biased human being – just try asking a computer and a 7-year-old to solve 32 x 8! One will provide an answer immediately, and the other will do everything in its power to avoid the question, have a snack and go climb a tree.

Although we have successfully created systems that can drive cars, understand human language, and play chess, ‘general intelligence’ (such as the kind possessed by our 7-year-old), remains out of reach.

We humans are irrational, inconsistent and creative – but this enables us to problem solve in a way that AI systems have not yet achieved. Computers have been specifically built and taught to tackle well-structured problems. That is, problems that have a clear goal and a set number of possible solutions. A current computer cannot ‘think outside the box’, in the same way we humans cannot imagine a brand-new colour – it simply is beyond the scope of our abilities.


Insight problems are problems that cannot usually be solved by a standard computational ‘if/then’ process.

In path problems (the kind a computer excels at), the solver is given a representation, which includes a starting state, a goal state, and a set of tools or functions that can be applied. In insight problems, the solver is given none of these.

The most famous insight problem was the one that led Archimedes to run naked through the streets of Syracuse. As the tale goes, the King of Syracuse thought that he had been conned by an unscrupulous goldsmith, and a recent commission did not contain pure gold. Archimedes was instructed to discover whether the king had been cheated. But how could he approach this problem?

Archimedes knew that silver was less dense than gold, so if he knew both the weight and volume of the commissioned crown, he could calculate whether the material was pure gold, or a blend. The difficulty was that the crown was an irregular shape, and therefore almost impossible to accurately measure.

Whilst pondering the issue in his bath, Archimedes noticed that the more his body sank into the water, the more water was displaced. He realised he could use this displacement theory to work out the volume of the crown. He leapt out of the bath shouting ‘Eureka!’- ‘I’ve got it’ and ran immediately to test his theory. The goldsmith was shortly accused of fraud by a triumphant (and presumably no longer naked) Archimedes.

With path problems, the computer can gauge how close to completion the task is. With insight problems, it is often hard to tell whether progress has been made, until there is a sudden ‘Eureka’ moment.


Here are the answers to the insight problems posted on our Linkedin page - @Business Systems International:

1. Here is a sequence of four numbers: 8, 5, 4, 9. Predict the next numbers in this sequence. The answer is 1, 7, 6 – the numbers have been arranged in alphabetical order

2. There are individual brown socks and black socks in a drawer in the ratio of five black socks for every four brown socks. How many socks do you have to pull out of the drawer to be certain to have at least one pair of either colour? Drawing two socks is obviously not enough because they could be of different colours. The ratio is a red herring. You would only need to take out three socks to have a pair of either matched pair of either brown or black socks.

3. Can you walk through the city of Kaliningrad, crossing the seven bridges each exactly once? In the map below, the bridges are marked in grey. It is impossible. Kaliningrad is divided into four regions (two riverbanks and two islands) and is served by an odd number of bridges (seven). Every time one enters a region by a bridge, then one must leave the region by a bridge so the number of bridges must be an even number to cross them all exactly once.

4. Imagine you are in a room with two strings hanging from the ceiling. Your task is to tie them together. In the room with you and the strings are a table, a spanner, a screwdriver, and a lighter. The strings are far enough apart that you cannot reach them both at the same time. How can these strings be tied together? The tools are a distraction. Regardless of their use, you can simply tie an object to a piece of string to form a pendulum weight, and then swing and catch it whist holding the other string.

5. Let’s say that to buy a bat and ball costs £1.10. The bat costs £1.00 more than the ball. How much does the ball cost? The ball costs 5p. Most people instinctively want to say the ball costs 10p, but if that was the case, the total cost of both items would be £1.20. One pound is only 90p more than 10p. In this question, the bat costs £1.05 and the ball costs £0.05.


The neurotypical human mind has two main systems of processing. The slow, deliberate, and accurate system is engaged when we solve a maths problem like 45x17. The fast, automatic, and relatively inaccurate system is used when we see a photograph of an angry person and immediately recognise that they are angry. The former requires calculated thought, and the latter pops into our mind without any conscious effort.

The former system is very close to our current standard of Artificial Intelligence. The latter is something we will need to build into our future technology to allow AI to ‘think’ as creatively as a human.

Rapid learning in this way might result in hasty generalisations which will need to be kept in check (see our article about the flaws and biases of AI), but it is an important step in allowing machine learning systems to learn creatively, rather than needing to be fed vast amounts of data.

It’s important to keep a realistic view what of the actual capabilities and potential of computers is. If a computer just needs to use its analytic capabilities to solve problems, then we have already created an instrument far superior to our own brains. However, as the insight problems in this article show, the human brain is capable of divergent thinking, common sense, and creativity – things which a computer cannot emulate. I think we don’t need to be worrying about a robot-uprising for quite some time yet!

As Alan Turing said in 1950, “We can only see a short distance ahead, but we can see plenty there that needs to be done.”
To effectively run AI systems, you need the highest performing hardware. BSI offers various types of AI optimised servers running on GPUs, which can all be configured to your exact specifications. You can find out more information on these solutions here or by getting in touch on +44 207 352 7007.


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