Naked Science - Intelligence

Copyright Michael Curtis 2020

All rights reserved


Part 2 


How can mistakes be spotted just before we are about to make them? The answer surely is to develop a habit of frequently challenging the truth of the statements and plans racing through our minds.


A Mistake Diary

Good thinking habits need to become a natural part of the way you think in everyday life. One way to focus the mind on thinking in these ways is to keep a diary of the mistakes you make as well as a diary of things you did inefficiently that you later realise you could have done in a better way. By analysing these events you can figure out what you should have been thinking rather than what you did think.

e.g. A person comes towards you and you expect the person to walk past you but the person stops and enters a phone box [another 1990s paragraph! We hardly see phone boxes nowadays!]. Your mistake was what?:

Believing an expectation without seeking evidence to support the prediction of where the person would go;

making a simple model of the paths the person could walk. The phone box was not considered to be an option. This limited your ability to ask, "Which one?" about the possible places the person might go to.

The diary provides material for you to practise the new habits with.


Done and Dusted

I work with spreadsheets a lot; and some tasks involve repeated data entry over a few hours. It might be that some maths in a cell needs editing; and there are 100s of cells which need finding and editing.

Sometimes, I stop at a cell on the spreadsheet and have a break. I make a hot drink and come back. I can move to the next cell and start editing that. This risks the ‘Done and Dusted’ mistake: I am assuming that, when I went for my break, it was after I did all the editing necessary on the cell that the cursor was on.

What if I was so tired of concentrating that I decided not to do the current cell, then went for a break, and came back to the unfinished cell? By me now moving on to the next cell, there is an unfinished task but I am blind to it.

Daily activities break down into steps where you might miss a step and not notice it; forgetting to take your door key with you is a good example of that. You might actually be leaving your home and thinking, “Do I have my key?” and having a weird certainty that you have your key despite not actually checking your pocket for it. We are good at convincing ourselves that all necessary checks have been done. Intelligence leaps if you are able to develop a less “one two miss a few” approach to the ‘beliefs’ that swim across your mind.


I’m Sure I’d Remember

I walked a path as exercise; and it is a path which I hardly ever walk along. I saw it branch off and I wondered if I could detour from the path and join up with it a little further along; but I couldn’t remember if the detour does rejoin the path.

And one of my thoughts was, “You’d definitely remember if the detour track eventually joins back with the main path; after all, you’ve walked it once before and your memory is good enough to remember a route back to the main path.”

And now I am imagining where the two routes might come together; and then I am unsure if this is something purely imagined or half based on a dim memory of a real rejoining track.

I’m sure I’d remember” is a false argument; but so is, “I am imagining the route so well that it probably really exists.”


Focused Attention

 A person can not think about 2 things at once [Ask a psychologist! People just think they can]. If you are not focused on a goal and why you are doing it then your logical reasoning is more likely to fail. By concentrating on the whole of a problem, there is less chance of you tackling it inadequately. Concentration is something that can be improved by doing tasks which require concentration (e.g. chess).

As an aside, I don’t like playing chess nowadays but, years ago, when I had nothing to do, I had a chess computer game and it helped to kill the time. It was very good for making me see that my mistakes had a pattern to them; and that they could be reduced by good habits.

I wonder if people have a biological genetic advantage in their ability to concentrate. Like you get naturally fast runners who I could never beat despite training like mad. Actually, I don’t wonder it; I am pretty sure of it. Add to that, you hear of how the things we eat and drink can lower our concentration: lifestyle.

I also believe that some people have a short powerful memory a bit like ‘photographic memory’ but of short duration. They can do mental maths better because numbers don’t slip into the wrong place; the carrier of 123 is not, some seconds later, remembered as 23. And so they don’t make so many mistakes; and then their concentration is free to work on the task rather than having the ball and chain of slowing down to deal with many mistakes or simply arriving at the wrong answer.

Realising that one’s concentration is below average, one can think about lifestyle diet; and think about forcing more breaks than an average person would have. Having said that, psychologists encourage anyone to take short breaks for the sake of concentration to be ok over a day’s work.

But lacking that natural advantage of powerful memory is a tough one to compensate for. I suppose we must recognise our limitations and then have a strategy to limit their effect. We can’t be as good as the naturals but we can be good or quite good – and certainly better than we were.

I read about famous savants; and some of them became less capable in adulthood. A wider theme here is that we probably need to review our own score of how good our memories are and how good our mental faculties are: age can surely change our natural capabilities.


Thinking Time

 A problem can only come to a sound conclusion when enough time has been spent on it. Coming up with a fast answer is not as a rule better than coming up with a well considered answer over a longer period of time.

There is a bad habit of ‘talking before thinking’ or seeing a preliminary answer and stating it without having the good habit of holding the thought and criticising it before stating it; the answer is double-checked by considering if the problem as a whole has been understood correctly and considered fully.

In chess, it is the habit of being reluctant to let go of the piece you are moving: have I missed something? It feels ok to commit my move but let’s have a final check.

With a business email, it is perhaps opening the email attachment you are about to send in order to double check that it is the intended file.

Again, we bob through life generally successfully without the extra discipline in our thinking. So it is quite a detour to dedicate oneself to better thinking habits. 


How many thoughts we can hold in our heads


The cognitive psychologist George A. Miller is famous for writing about the topic of how many concepts one can work with simultaneously without tending to make errors.

For different people, the number varies; and it is not, in my opinion, a very high number.

I came across Miller’s name when I was studying computer programming. You can write a quite complicated paragraph of code and call it by its name such as ‘do the 10 steps of maths’; although there are 10 things going on, I have chunked it together into one routine of code to call. In that way, my mind is freed up and thinking about one thing even though 10 things are going on.

A driver might not need to think about the streets route he will take when he is at the next town; for now, his task is to think about the streets necessary to get to that next town. Overall, he will be travelling a lot of roads but he is thinking about a small number of them at any one time.

It is good to remove clutter where we can so that our attention is focused on a small number of items. Accuracy is then a lot more likely.

As an aside, computer programming can be very hard. There is something called a compiler which tells you at which line your program code that you typed is not consistent with the rules of the computer language: it is telling you where the program would go wrong if you ran the code. This debugging process often involves the computer telling you a hint as to which line the error is at and what the nature of the error is. It can be a real headache because the error might actually be at the line above the line it has told you is wrong; and the hint can be wildly misleading too. I suppose it develops a discipline in me of taking matters into my own hands: “Never mind what you’re telling me, I’m going to try to shine a different light on the problem.”

Beyond that, there are mistakes which I make in my own logic; and also there are lines of code which the computer thinks are perfect (and so it does not report them as wrong) but they are mistyped words by me.

In the same way that I recommend chess as a way to think about thinking, I would recommend computer programming too.


What Is Thinking ?



This chapter looks at the background of what it is to think. It will introduce some useful vocabulary for describing the world around us or useful vocabulary for describing the concepts we are playing with as we think.

Of course, this is just me writing. I’d be very dubious of anyone telling me what thinking is. It can be all sorts of things!


When Do You Think ?


Thinking’ is a Tool

People want things. They think in order to get what they want: thinking is a way to ACHIEVE their GOALS. A lot of thinking is not done as a way to ACHIEVE GOALS. It just happens. It is good that thinking just happens because it brings to our attention our desire to ACHIEVE some GOAL or information which might be useful for ACHIEVING a GOAL.


An Example of GOAL-SEEKING

Some facts;

Shoes are worn on the feet.

The butchers sells meat.

The shoe shop sells shoes.

The barbers does hair cuts.

The sun is hot.

The shops are shut on sundays.

GOAL : - I want to buy some shoes.

Note how the GOAL directs thoughts towards facts and ways of using facts.

My thoughts :- I consider facts which relate to shoes. Some may be irrelevant to the buying of shoes by me. I consider whether today is a sunday because that information is relevant to deciding whether a shoe shop can sell me shoes.


Facts, Rules, Classes, Uncertainty

Note: I can imagine people holding me up on minor points but this is how I imagine very clever people abstract the world: their ‘vocabulary’ while they process information involves something like this language.



A fact is capable of being true or false. e.g. "I own a car." I either do or I do not. Facts have some of these qualities;

Structure: An object has shape and size and is made of some material. E.g. A car of metal, an apple of organic material.

Direct function: The car has wheels which turn, an indicator switch which switches, lights which turn on or off. The apple ‘grows’. These are functions which are directly related to the structure.

Indirect function: The car can be seen as being an isolated thing: it is a SYSTEM. The apple can be seen as being an isolated thing: it is a SYSTEM. SYSTEMS can interact with a CONTEXT. e.g. The car touches a road. The wheels turn on the road’s surface. The turning of the wheels is a direct function but the act of ‘driving’ involves the road ( CONTEXT) and so ‘driving’ is an indirect function. A room in a house is a SYSTEM and the overall house is its CONTEXT or, I suppose, a bigger system. In that example, the SYSTEM is part of the CONTEXT.

Purpose: What is the car’s purpose ? Perhaps to transport the driver. What is the apple’s purpose ? Perhaps its use as food. The apple might be used as a ball for a game. So, purpose depends on the GOAL of a person. If I want to play then the apple’s purpose is different to its purpose when I want to eat.

In contrast, FUNCTION is ‘how the STRUCTURE CHANGES STATE’. Sometimes, function ACHIEVES PURPOSE. e.g. The ‘being eaten’ function of an apple helps me fulfill my desire to eat. Or, the ‘wheels turning’ function of a car allows me to drive. I will use the word GOAL when talking about an aim or desire with many objectives to it. e.g. ‘Travelling to work’ is an aim or GOAL and it has many objectives to be met.

I travel to work by using a pavement with its PURPOSE as a

medium for travel, I use a train with its PURPOSE as a medium

for travel. So, a GOAL is a desired result while a PURPOSE is why a SYSTEM like a train is useful for achieving the result.

Location: Structures have location. There can be a CONTEXT like a garden where there is a flower (structure) and grass (other structure) in that location.

Label: A name is given to things. You can call a bed a ‘lit’ in French but it is a bed regardless of the name you apply to it. Labels are useful for the communication of information or for noting information.

Language problems occur when labels are misread or misheard, misinterpreted, or mean many things; or a meaningless utterance might be interpreted as being meaningful.

Concepts: Emotions and moods are ‘feelings’. Being thoughts, they might be thought of as being aspects of the brain’s structure and function but they do not have their own structure. A concept like ‘music’ also lacks a structure and yet all of these concepts can exist in the mind. In addition to this, structures, functions, etc. can be thought about and so they are capable of being concepts too.

I will sometimes use the word concept to mean those intangible things but I will also use it to mean, well, .. concepts: the stuff I am thinking about – which are, as thoughts, intangible too.

Relationship: One SYSTEM can be related to another SYSTEM. e.g. "The man eats a sandwich", relates the man to the sandwich to eating. Relationships can be indirect. e.g. A man in India can be related to a man in England by the fact that they each take trains regularly. This is a loose tie between them : an indirect relationship.

Symbolism A SYSTEM can symbolise a meaning. e.g. A road sign of meaning: a sign about men doing work is not the same thing as literally men doing work but there is a meaning to the sign which alerts us to be on the lookout for road works.

A symbol is capable of being misinterpreted. e.g. ‘X’ on a page might mean a letter sound or a mathematical multiplication.

A symbol might not have been intended to be a symbol by anyone. e.g. Three fallen twigs might land in an arrow shape and might be believed by a passer-by to be an arrow placed there to guide lost people.

Note that labels are a type of symbol.



"Sarah is always late" can be expressed as "IF Sarah is here now THEN Sarah is late": ‘Sarah is here now’ (a fact) goes hand-in hand with ‘Sarah is late’ (another fact). A sentence expressible as "IF [fact1] THEN [fact2]" is a rule.

A rule like the above one allows you to know a fact as a result of being given another fact. e.g. the ‘Sarah is here’ fact must occur with the ‘Sarah is late’ fact.

Mistakes involve belief that an assertion is fact but really it is not.

I have told you that Sarah is always late but maybe I have ‘an axe to grind’ and am trying to give her a bad reputation; she might really be quite a punctual person. Once you believe me, the possibility of mistakes opens up. Your fact chain of ‘A goes hand-in-hand with B’ is perfect and logical but the quality of a fact is bad. 



A car, a bicycle, and a boat are all vehicles. The idea of a ‘vehicle’ is a CLASS of which the car, bicycle, and boat are specific EXAMPLES. The CLASS is a fragile idea of what is ESSENTIAL in an object for it to be an EXAMPLE of a vehicle.

A bed is not a vehicle because it lacks the essentials of a vehicle (by my personal definition of what a bed is and of what a vehicle class is). Similarly, a cottage, block of flats, and shop are all EXAMPLES of the ‘buildings’ CLASS.

Sometimes, there are different definitions of what are the ESSENTIALS of a CLASS. I might claim that a car must have four wheels for it to be a car. You might claim that a three-wheeled type of vehicle can still be a car. Someone else might say that a toy car is a car. So, there may be an unclear or FUZZY idea of what a car is: and people talk of semantics. This FUZZY definition of a CLASS allows me to say that a radio is nothing like a car but that a van is much like a car, and that some things might be cars while a Rolls Royce I see definitely is a car.

Note that EXAMPLES can themselves be CLASSES. e.g. There are many types of Rolls Royce. So, ‘cars’ is a CLASS with Rolls Royce as an EXAMPLE while Rolls Royce is a CLASS with many EXAMPLES.

Note also that seemingly unrelated items can be members of the same CLASS. e.g. An iron, a chair, and a balloon are all ‘things in my home’ and so they belong in a class despite not being very similar at all.

Something I’ve been pondering is: if a lot of people start using a word in a particular way then it somehow becomes a true definition of the word; or at least has enough plausibility to be taken seriously as a meaning. For instance, a lot of people say in early May that the weather is Summer weather; but purists might say that Summer begins later in the year: we are still in Spring. The weather is similar to June weather because it is nice and sunny – in a way it is Summer weather – enough for me not to argue with people for calling it Summer weather!

[I guess a good thinker would have a cached memory that Summer in one hemisphere is Winter in the other; and ideas for deductions would float across his/her mind]

I think that it is hard to follow a conversation if mental time is spent checking definitions and probabilities of what people are stating. Someone states that something is ‘good’ or ‘bad’ and you either accept the statement at face value and listen to the next thing the person says or you partition the conversation into the part you are evaluating and the new part arriving – how can that work cleanly?!

What if someone uses two contrary definitions of a word while the conversation progresses? It all gets very messy!



We tend to think with a GOAL in mind. We observe the world or recall memories and think about ideas. Sometimes, we come across UNCERTAINTY like ;

-         I am not sure if my observational abilities are accurate. e.g. Poor eyesight or watching a fast-moving object.

-         I am not sure what CLASS the item I am observing belongs to. e.g. Is the person in the distance a child or an adult ?

-          I am unsure if a rule is true. e.g. "If I jog often then I will be healthier." Maybe this is only true for some people or not true at all.

-         Someone talks about a CLASS - by pronouncing its LABEL. I am not sure that my definition of the LABEL has the same ESSENTIAL ingredients as the talker thinks it has. e.g. One person thinks the phrase ‘good musician’ means someone who sounds good on an instrument but I think the word is probably being used to mean technical accomplishment on an instrument even if the music played sounds bad to me.

Mistakes occur when we do not spot that something is uncertain and believe in it. e.g. I might believe that a good card player is just lucky ; but without valid evidence I should not believe the idea. Or, I might see a child-like person in the distance and decide that the person can not be an adult - without proof!

UNCERTAINTY is difficult to think about because it can so easily slip the memory that an idea is not PROVEN with VALID EVIDENCE. I can imagine the person in the distance to be a child, a white child, a white boy, but I have to distinguish a PLAUSIBLE concept from what is CERTAIN and remember that the imagined concept is not PROVEN.

Weak concentration and the low limit on how many concepts we can juggle in our minds at any one time exacerbate the problem of evaluating what is certain; and remembering the uncertainty score that we have given something. If I forget that I am dubious of a ‘fact’ then I might just remember the fact and use it in my logic. So that Miller’s number idea of how much we can safely juggle in our minds is a huge problem for you humans.


Using this vocabulary

You have now come across the following terms;


























This vocabulary can be used to describe difficulties which people encounter when thinking. Very important points in this chapter are ;

1). It is easy to mistake a PLAUSIBLE CONCEPT for a PROVEN FACT. When something is PLAUSIBLE, it is easy to believe it.

Good thinkers have the habit of challenging the VALIDITY of their thoughts - even when facts seem obviously true.

2). There are GOALS which people aim to ACHIEVE by pursuing sub-GOALS or objectives.

Some GOALS are more important than others. You might succeed at one GOAL by spending time that should have been spent on some other goal. Also, a sub-GOAL might cease to be important because of a change in circumstances (like trying to score in football after the final whistle). I call that TRUMPing: situation A has been TRUMPed by situation B.  Good thinkers have the habit of regularly challenging the worth of pursuing a GOAL or sub-GOAL and thus avoid wasting or misusing time.



Mistakes Again



Remember from earlier on that a mistake is the result of putting misplaced trust in a thought’s validity. e.g. If today is February the 24th then a week from now it will be February 31st.

Later in this book I look at mistakes people make when listening to people, and mistakes people make when doing basic mathematics. However, there are general errors which tend to creep into our thinking. I want to look at those first.


Exhaustiveness and Variety



If I have two dice, and I roll them, what are the possible outcomes ? You can start to answer the question by imagining outcomes and writing them down. e.g. 6 and 1, 4 and 3, 2 and 5. Or, you can write 1 and 1, 1 and 2, 1 and 3, 1 and 4, 1 and 5, 1 and 6, 2 and 1, 2 and 2, and so on.

The second method is desirable because it makes it easy to list every combination of dice rolls whereas the first method can take longer and lead to uncertainty as to when (if at all) all dice rolls have been written out once.

It’s the sequencing – starting at 1 and then progressing to 2 that matters.

What is good about the second method is that it is exhaustive: it exhausts all possibilities; and it does it in a methodical way.

One problem you humans have with thinking is that an idea of ‘how things are’ enters the head and it stays there unchallenged. e.g. a belief that your door key is in your pocket when you leave your home (but you do not have your key on you).

A good thinker has an awareness of the illusion of correctness that is often present in ideas of ‘how things are’. A good thinker challenges his trust in his thoughts’ validity. This is a habit that anyone can develop.

You could set aside time in your day to look around your surroundings, make statements about what you see in front of you and then play with the idea that you might be mistaken. Or deliberately make untrue statements about what you see in front of you; and imagine how you would pick apart the untrue nature of the statement if someone were to state it to you.

How could the thing you are certain of be wrong? Like a kitchen cleaning product might be pronounced wrongly by you because it is from another country where the alphabet is pronounced differently; and does that really make your pronunciation wrong?...

Note: A major threat to our ability to think exhaustively is a habit of ours to assume that a question only has one answer.

e.g.-1 What even number below 5 divides into 12 exactly? 2 is a correct answer but it is not the only answer: 4 is correct as well.

e.g.-2 I ask someone,’Where do you live ?’ and expect one address as the answer but the person lives at three addresses. This manyness or plurality is hard to anticipate.

What is required is an exhaustive approach which looks for a 2nd answer and then for a third until all possibilities have been explored.



There are classes of objects. A bear might be said to belong in the animal class, for instance. If I start talking about animals and you imagine a bear because it is an animal then I ask you what characteristics animals have, you can use the example of a bear to give me valid characteristics. However, a bear is not entirely like a tiger or a bat and so many characteristics of animals will not be given if you stick to just imagining a bear while listing characteristics of animals.

Furthermore, after a time of answering my question by imagining a bear, you might forget the original question and just assume that the question is ‘What are the characteristics of bears?’

What is required is an awareness of WHY you are imagining a bear: the GOAL you are trying to ACHIEVE. If you have that habit then you can move on to discuss characteristics of other animals.

Let us call ideas which get stuck in the head without valid justification (like the bear) a STATIC idea.


Where Do Static Ideas Come From?

Continuing with the bear example: The following are some reasons for a bear image to appear in the head rather than any other animal, and why I imagine a particular bear instead of a wide range of types of bear in different situations..



We often picture simple ideas. e.g. Someone says,"I drove to work this morning", and I imagine the person driving in his car alone even though he might have been driving his children to school on his way to work. The children are an additional detail. My mind just chose a simple image without children. And why a car? Why not a van?

It is alright to imagine the person driving without passengers provided that you are aware that the person might have had passengers.

Another error I might make is that I imagine the person in the car he is known to drive but today he took his wife’s car to work instead of his own (it is being serviced). Again, it is alright to imagine the person in his usual car provided that there is a question mark against that detail.

I think that some people are naturally good at abstracting what they are thinking about – they have a head start on not being constrained by static images.

Question marks allow us not to believe ideas too much even though the image of the man driving to work in his car is vivid within my imagination.



If I am asked to think of a comedian, I am perhaps more likely to say the name of someone who I watch on television often or one I have thought about often rather than a comedian who I have only seen a few times. The familiarity of the comedian makes him spring to mind.

There is simplicity in imagining familiar things. e.g. When I imagined my friend driving, I imagined him in his own car partly because that is a familiar image. Question marks allow us not to believe too much ideas which spring to mind.


Not recognising a contradiction

Your powers of observation can bring to your attention clues that your ideas are wrong. e.g. You plan to go to a party on Sunday and you think today is Sunday. Your calendar highlights today as being Saturday. Good observation might make you observe the calendar and possibly ‘set the alarm bells ringing’ in your head so that you question your assumption that today is Sunday.

It is not enough to casually observe Saturday on the calendar. Some kind of significance awareness needs to fire in your mind to stop you from still thinking today is Sunday.

If you have a habit typically questioning fact assertions, your mind would be thinking, “My calendar states Saturday… but is it really Saturday?”; and then hopefully, another area of your mind answers, “No, because I know today is Sunday” and then hopefully your mind challenges: “How do you KNOW that today is Sunday?” and then suddenly you awaken to the fact that it is Saturday today.

In short, the habit of questioning, all the time, leads to more powerful thinking.