You Are Statistical; Resistance Is Futile
Quick: Which of the following pictures has more people?
You can almost instantly recognize that the left has the higher number of people. But how many more people does it have? Now you’re stuck. No number naturally appears in your mind, unless you focus your attention and count each person one by one. It doesn’t have to be people; you can also try “green leaves”, as in, which picture has more “green leaves”? You might be quite ready to say the left one. Here comes the contrasting question: How many green leaves does the left picture have more than the right? Oops. But if you don’t know how many more green leaves the left picture has over the right picture, how can you be so sure the left picture has more green leaves?
Why is it that you can easily tell at an instant which scene has more items of a given kind than another, but find it very hard and energy draining to give the exact numerical difference? It doesn’t matter whether you are good with mathematics or not. It doesn’t matter whether you are young and energetic, or mature and more lethargic.
Further, it’s not just with sight; it is evident with other senses as well, like sound, smell, taste and touch. In a choir with mostly female voices and only a few male voices versus another choir with mostly base voices with a few sopranos, you can tell which group is which almost right at the first few notes but you cannot tell how many male and female singers exactly. Between two dip sauces, one is with mostly chilly with a dash of soy sauce while another has mostly soy sauce with a bit of chilly, you can tell almost immediately when a drop of each is placed in your mouth but not the quantity in milliliters or grams. Or, recall the last time you touched someone’s forehead and concluded, correctly, that the person had fever, but were not sure exactly how many degrees Celsius the person’s fever reached. Why?
Why is it that we do not have an inkling of an idea the quantity of the measurement upon which we make our judgments? Doesn’t the wise saying go something like, “if you cannot measure, you cannot manage nor act”. So why are we able to manage and act on the right thing without knowing the exact quantitative difference?
The answer lies deep within us. It’s how we are made. It is a fruitless attempt to try to change our way of thinking by insisting that we obtain numerical quantities first, then compare the numbers to realize which has more, and then decide – we are not made like that.
You are statistical, and resistance is futile.
Our senses interact with reality in a “bulk” and statistical way rather than in a refined and detailed manner. Unlike computer chips, we don’t count, compare the numbers and then make decisions; we kind of do all at once without knowing how. Take the picture comparison exercise again, for example. We don’t count the people on the left picture, then the right picture, and then compare the counted numbers and then decide and conclude. A computer program might do that and report precisely how many persons more the left picture has over the right picture. We cannot do that. Try to slow motion yourself into the whole process and see if you can capture the moment your brain has gained awareness of exactly how many people are in the left picture and the right picture. It is not possible without fundamentally changing your processing by counting one person at a time and taking much longer to answer what was supposed to be an instantaneous answer.
Our mind is statistical in the sense that you could give a different number the next time you try to estimate it again. Also, asking different people the same question would almost certainly yield different estimates when the answers are nearly but not exactly the same. In our example above, it would be like showing two pictures in which one has 151 people and the other has 120 people, both are plenty of people to squeeze into a picture. A computer program would count the number of faces exactly and be able to tell that the 151-people picture has thirty-one more people than the 120-people picture – but not us. We’re a statistical processor. From the sensors (the retina cells) to the nerves and finally to a conscious decision to choose which picture has more people, our body obtains a series of statistical outcomes which ultimately tell us to choose the picture which we perceive as having statistically higher number of people. It is beyond our ability to “debug” our chain of statistical reasoning by asking our retina cells, “how many human-shape features have you detected?” Or asking our brain cells, “What number did you get from the retina? How many people have you counted? How many non-human features have you filtered off? What is the net count?” We simply do not have a number at all, despite being able to pick out the image with higher people count, most of the time.
Saying we are statistical is different from saying we are estimating all the time. If we were like a computer robot being asked to estimate, then following the same steps of estimation algorithm, we would always give the same estimated number, regardless of when you ask or who you ask. But we are certainly not robotic and do not always give the same estimated number all the time. Shown a picture of a stadium full of people and asked how many people there are, one might say 10,000 the first time. Shown another time on another day and occasion, the same person might say 12,000. Since even estimates can change, our minds are not running estimation process, but instead, statistical processes.
If a computer software is programmed to make a quick estimation like human, what it does is that it would always provide the same estimated number of people if it is given the same picture. Furthermore, different computers or brands running the same algorithm would always output the same estimated number of people. If the answer to number of people in the stadium is 12,732, you will get the estimated answer 13,000 whether you run Python, PHP, C++, Java on Windows, Mac or mobile phones. The deterministic procedural nature of how computers are designed and programmed requires this consistency to be the characteristic. It turns out that if a computer sometimes estimates 10,000 and sometimes estimates 12,000 like people do, it would be considered a “bug” – an undesirable flaw uncharacteristic of a computer.
We Are Statistical At Cellular Level
But we’re almost the opposite.
We’re inherently statistical in nature – given the same objective signals like sight or sound, we might perceive these signals as significant most of the time, but not always and not always predictably. Remember the last time you tried to send a mobile message like,
“I don’t think I’ll be able to reach on time”
and found, to your horror, that you’ve typed
“I think I’ll be able to reach on time”?
No, the mobile phone’s spelling auto-correction has been turned off. During typing, you had clear impression that you saw the word “don’t” being typed properly. Yet, this happened. It is not a proof that we’re statistical, but it does support the notion that we don’t always “see” what we think we have seen.
Our perceptions of reality, whether it be sight, sound, smell, taste or feel are dependent on our signal receiving organs like eyes, ears, nose, tongue, skin and muscles. The energy that powers your body organs and the transmissions of signals through the nerves comes from a statistical source – the blood stream. Billions of blood cells transmit energy – comprising oxygen and nutrients – to billions of cells. While the numbers might sound astoundingly huge, the close encounter of how a cell receives energy from blood cells is a totally different story.
Suppose you are thirsty and you need water like the way your cells need energy. One way to quench your thirst is to drink from a water tap. With proper positioning, you tend to get some 99% of the water coming out from the tap. Or, you could spray water jet into the air, and try to catch water droplets falling down. Your body cells get energy from the blood stream in a way that is more similar to the latter than the former way of drinking water. Blood cells deposit plenty of energy into a reservoir so that most cells have high chance of getting what they need in due course, BUT, there is no guarantee that when a particular cell needs an extra pack of energy at a particular time because of the need to do decision, the cell will definitely get it.
Say if now a cell needs to get more activated because it needs to electrically deliver a signal or just do something to indicate its decision to choose the picture with more perceived people, it is a probabilistic process as to whether the cell could actually end up getting the energy pack or not. If a decision process is such that without the extra energy, the cell fails to fire up, it would result in a decision as if the cell had chosen not to fire up and the picture with fewer perceived people would be chosen as the answer for a question asking for a picture with more people.
Since we are made up of billions of cells all requiring supply of energy, this statistical process of energy transmission translates into a statistical process of making decisions. It permeates throughout our body, and dictates how we think, communicate, behave, walk, work, play sports, decide and live.
We Are Statistical Since Infancy
In “The surprisingly logical minds of babies”, Laura Schulz, an MIT professor, probes the statistical minds of 15-month old babies [1]. You are reminded that babies haven’t learned about counting “one, two, three” the way we do, yet. In her presentation, Laura illustrates how babies perceive “many” and “few”, and effortlessly decide on different strategies to react to a given object like a yellow ball with a stick in conjunction with the perceived probability of similar events occurring.
The experiment hardly looks “surprising”, until one looks at the experimental results Laura shows. The expected logical reaction was performed by 80% and about 65% of babies who participated in the two experiments – babies are not behaving robotically and can exhibit unexpected illogical reactions which are different from what majority of babies show. They are raw statistical processors analyzing big data from visual and audio senses and distilling them into a statistical outcome that most likely is the correct action for them.
We continue to be statistical as we grow. When one or two bees fly toward you, you stick to your ground and might even swing your arms in an attempt to fling them away. When a swarm of many bees fly toward you, your mind does not count “one, two, three, … bees” and arrive at a big number before your body starts to turn and run for your life – we just don’t do that. When a dog runs towards you showing its teeth, you might stand your ground (or you might also run). But when many dogs run towards you, you don’t count “one, two, three, … eighteen dogs” and check that eighteen is more than a threshold of three before you start running away. One look at that many dogs and our legs immediately would run.
Implications
Recognizing that we are statistical has implications on the way we communicate, learn, and make decisions.
In communications, we might not like the act of repeating ourselves twice, not to mention many times the same sentence, statement or idea. So we prefer and encourage conciseness – saying one intended meaning once and using as little words as possible. But because people perceive your words statistically, there is no assurance that what you meant to say was actually perceived by your intended audience. Each word has a distribution of meanings in which certain meaning might be the most likely meaning (ie the “mode meaning” in statistical speak) you have intended. However, the same word may also be perceived as another distribution of meanings where the most-likely meaning is another meaning which you have not intended. As such, miscommunication could result with undesirable consequences, whether it is losing a business deal or a friend. So if clarity is intended, it could be a better way to communicate with some level of repetitions to reaffirm the intended meaning.
In marketing, the same advertisement is repeatedly played during various time slots over several channels. In some occasions, the same advertisement is played in television channels, movie theatres and social media ads. This is repeated until one could hum the advertisement’s music, or chant the same slogan as what the advertisement says. But wait – since when have we sat down to study or memorize the advertisement’s music or slogan? We did not. Yet we could recall effortlessly what the music or slogan was. Whether it is a good product or bad product, at the risk of irritating audience, this repetition actually works. It takes advantage of our statistical mind which silently notices the “many” advertisements being shown to it as the “norm”. If the ad is about shampoo, won’t you buy the “norm” shampoo instead of risking an unknown brand? If the ad is about a particular baby milk powder, won’t you buy the “norm” milk powder instead of risking an unknown brand?
In learning, we might question whether rote-learning – a method of committing information to memory through repetition – is really a bad thing. If unwanted messages from advertisements work so well on being retained effortlessly by a large audience after many repetitions, how would rote-learning important foundation knowledge be a bad thing? I am not promoting any virtue of rote-learning. But given that our statistical mind “takes note” automatically of “bulk” messages – information that occur frequently and possibly repeatedly over time – perhaps rote-learning has some roles to play in learning. Could some form of modified rote-learning be a better fit to help us quickly remember messages, information and knowledge?
In making decisions, we often “learn” to trust scientific reasoning and to ignore or play down our gut instinct. But instinctive reaction based on our statistical mind, or a “hunch” as we often call it, often surprises us as being powerfully correct. Have we perhaps unnecessarily over-stressed the logic of scientific reasoning over the correct instinctive decision we naturally possess? When we “learn” to apply assumptions-based scientific decision tools in business classes by encoding coarse discretized information with Greek symbols, have we “unlearned” or ignored our far more complex and comprehensive instinct and gut-feel which might have made much better contextual decisions?
Could it be that the level of science as we know it has yet to be able to even explain why our instinctive decisions based on statistical senses and thought processes are often not wrong, so much so that an easy way out is to assert that decisions based on instinct are not accurate?
We are statistical, at cellular level and since infancy. Instead of resisting our innate nature with futility, it might be better to nurture, strengthen and build on our statistical being.
Chin Chee Kai
[The above article is written to share with my past students as a form of continuation of academic exploration, discussion and learning, for them and for me, too. Feel free to comment, agree, disagree, correlate, expand, annotate, give counter-example, etc.]
[1] https://www.ted.com/talks/laura_schulz_the_surprisingly_logical_minds_of_babies#t-615405