Why (much of) math at school may harm.
Let’s do a thought experiment with Math. Something deeply disturbs me about it, ever since making sums at school really put me off. Ever wondered why when asked, what is 23 x 156,4 many people’s mind go immediately blank? Then I couldn’t explain why. They told me it might be low intelligence. I personally long thought I couldn’t think abstract. I now think it was something deeper and more real. Perhaps down to the neurological level. Something that hurts children when forced to do too early, something that may be way less real than we assume.
Take five apples. Put them in front of you on a table. Five apples right?
Current mathematics might be terribly flawed. I mean how we deal with it, not the logic behind the calculus. I wonder if this abstract art even helps create wars and famine, and worse, stops all real efforts to stop the ecological disaster. Let’s investigate.
Note: I explained this post to a friend in education. Because of this post he suddenly understood how abstract mathematics in early childhood (Yes, even stuff like 12x12) forces children to disconnect from their real world experience. Many get or feel lost because of this. It explained to him how this hurts children. They feel being lied to, or sucked into something that feels wrong and therefore so many suffer in education. Consider this for yourself when reading onward.
“Arithmetic. We all must be able to do it, we think. That’s why we start as soon as possible with it at school. But what does it do? We lift children out of their reality and force them into a context free, abstract world to which they don’t feel any relationship.” ~ Lex Hupe, Educational Innovator
Is 5 really 5?
Look at the 5 apples again. Still five apples?
Accustomed to math you probably already separated these apples from the table, room, you and the rest of reality you’re part of. The reality is that there are five apples laying on a table with a human looking at them, within a wider context. Each apple is also slightly different from the others. Also, the value of those apples is not constant but relative. As we’ll see: context and definition may change everything.
Next to the context and definition there’s the reconstruction of those apples in your head. How do you personally see them. Perhaps a mix of red and green and or yellow. There may be a childhood memory popping up. All refigured to pictures in your brain. And then there’s finally the representation of these five apples into a number, a mathematical reality. We pretend they’re all the same when confronted with numbers. It all feels all the same. Only that it isn’t. And that is a fundamental problem. Fixed numbers are a deception. We only pretend they aren’t. That’s how we’ve been forcefully educated. And it’s a lie.
“A problem is never solved on its own level; being complex, it must be understood in its total process. To try to solve a problem on only one level, physical or psychological, leads to further conflict and confusion. For the resolution of a problem, there must be this awareness, this passive alertness which reveals its total process.” ~ Krishnamurti
The Reality Gap formula.
The fact that many people will stop reading this bit, because they will have a hard time relating is exactly the point. In that case read on after the picture of the fiver. For those that read on, it’s me trying to make the point against the effect of mathematics on most humans… using mathematics. ;)
The problem is we humans tend to think: Reality is the same as what my brain makes of my sensory input, which is the same as the mythical mathematical representation I use to symbolize that concept in my head with. Hey, it’s generally excepted when we talk money. This is what happens: We observe X in reality = then X is reconfigured (neurological in our brain) finally X = represented (we have reality framed in a symbol or word). Think five apple on a table = 5 apples in my head = 5. This X seems right, 5 appels, but is just a symbol representing a mathematical construct, pointing out a small aspect of reality, deeply separated from it.
The little superscripted double faced R means (multi-facetted) Reality, the backwards R Reality Reconfigured and the normal R Represented, read X turned into mathematical symbol. To understand a number really we must consider what influences our observation. For example, any reconfiguration in the brain may be influenced by how these people experience certain numbers. They may get neurologically happier when their lucky number turns up, or the date of their birth. Thus their observation of reality is changed and thus their relationship to it.
In this formula above the line, we consider the three Xr’s as the same, when in reality they aren’t. Below the line, differences become apparent. The bigger the gap, the bigger the problems. And trust me, though we expect them to be the same, the outcome always will have gaps, that create noise.
So each Xr is different from the others. X in reality ≠ X reconfigured ≠ X represented. The bigger the gaps between above and below the line, and in between the Xr’s, the more harm it can do. A calculated amount of collateral damage may be represented as 200 dead in the media, yet will in reality mean propaganda, mostly not telling about 10.000 people in mourning for these deaths. People who are now traumatized and or wounded because of the what the attack did to them. It means parents and children heartbroken. How could we ever see that as a ‘telling’ number?
Numbers only may seem solid, like with the 5 apples on a table. Yet if if no steps are taken these five will rot and your kitchen have dozens of fruit flies. These apples also mean something different to people who don’t get to eat, then to the accountant who is checking the numbers. Doing the calculations he forgets all about the context of people outside waiting for something to eat. What we consider normal math is therefore purely trained self-disconnection from context.
As soon as one person projects his Xr (perceived reality) as in reconfiguration of X in his head on another person’s Xr (Can you even guess which Xr is meant here?) trouble begins. We humans quite possibly even put an added estimated emotional value to the Xr further widening the gap with any Xr of another. This makes the idea of straightforward numbers weaker and less realistic. The numbers seem the same because of social compliance and lack of awareness by the players. Also when kids don’t play along with our lies about this, we call them stupid.
And if we include fuzzy logic (Yes, an actual serious part of mathematics and philosophy, look it up) then also true is both ‘X is X and X is not X’.
“The Tao that can be talked about, isn’t the real Tao.” ~Lao Tse
The problem of 5=5
We end up having no choice but to put every number in context. $5 isn’t the same $5 from one person to the next. Say a police agent fines a person with 5 dollars. For this cop, 5 dollars means he’s getting his target, and it’s only a fiver. But for the fined person that fiver may mean food that evening, or mean nothing when he has 10.000.000 of those in the bank. And if someone has 50.000.000 in the bank, but not on him, does he then have them or not? It’s like someone who knew Schrödinger’s cat was alive in the box, but currently, it’s dead to the police officer who opened it. All we know the fine says $5 and when it’s been paid, then the math says everything is alright. That’s how we learned to see math in school. If the poor man pays a $5 fine and he has $7,03 in total, then how much does he have got left to buy dinner for himself and his kids? The law of math and what feels like justice is punishing his kids. Does that feel fair? Police math says it is. Why don’t they teach us that the calculation doesn’t represent the full story?
Now we can see why poor people often cower when stopped by the police. They can’t afford to lose more. But very rich people, with no money on them, will get angry because of the fuzz over a fine that means nothing to them. One might even argue that thus equal fines for certain events, are actually unfair as they mean very different things to different people*. And anyone studying law should be able to tell you there are huge disparities between the punishment of different people. A black person, with 200 gram of illegal opioid pills on him, often gets a much heavier punishment than the white pharmaceutical company CEO who killed thousands of people, by getting his sales targets. The CEO may get off scot-free and a big fat bonus.
A number x, therefore, means x separated from the context it stems from. This means that any number, when applied as reality, may be very harmful. We all know stories of people who demand some exact number squeezing life out of others. Sharp calculations may make a plane engine safer, they also can bankrupt an economy when the context of the numbers, like in 2008, is forgotten. And 200 dead children because of a (probably botched calculation) drone strike isn’t just a number, is it?
*) In Finland you do pay different fines for the same speeding offense according to your income.
We act from our context and relationship with any given reality and any number. And context and relationship may change everything. Too often bankers confuse the representation of x in their register with the meaning or reality of x for a customer. Mathematicians will say that x=x, and that our emotions about it don’t count. But anyone near extreme greed or extreme poverty knows that context of a number influences its meaning and therefore creates different actions in reality. Thus x ≠ x.
And any time we insist to claim X=X we warp the truth and get more disconnected. Or as Lex Hupe says: “The influence of the mechanistic world view of Descartes and Newton still rule”. They rule even though outdated by many new insights, that show the interconnectedness of everything. most of us always translate numbers back to an opinion or viewpoint, because that’s how we relate. Being informed how wealthy I am may influence your opinion about this article. And it doesn’t have to be true, it’s what you believe. x ≠ x And when you ignore that fact, things can go very wrong.
We believed we’d be safe. We believed the chance that something like Fukushima would happen after Tchernobyl was less than one in millions. To other numbers we’ve become numb. The 75% loss of insect life on the planet in recent years is a global disaster**. Yet this number means nothing to the people, it’s too big to comprehend. It means nothing to the companies who keep selling the poisons that kill those insects. It means nothing to the politicians who listen to the corporate lobbies. We get exited about numbers that are unreal, we ignore essential numbers because we can’t connect. Because we all believe in disconnected crazy math. We teach, read drill, children to disconnect from context and reality to make their sums. We listen to numbers in the news and check how the the stock numbers change because of it. We forget, ignore, are disconnected from the impact on real people and our planet. No wonder the world is a mess. Yet, we keep going as long as the numbers all match up, isn’t it?
Note: After publishing this a friend on facebook sends me this link. Numbers are the worst thing to use to make change happen. I’d say because we’re emotionally disconnected from them. Bet you’ve already forgotten those 200 dead kids earlier in this text, let alone make you more pacifist. What would make a difference then? Follow the link above. ;)
Note: The first version of the formula didn’t have an outcome, see the ‘isn’t 1' at the end. I improved the formula with the help of Predag Končar, a mathematician.
Note: If you want to read on or know more, check out this article on science. It shows how science can’t really advance because of a similar disconnection. By the way, this post was published before on this blog.
**) This article was published in 2017! Did you hear of it? Even the Guardian posted about it. But no government actions I heard of, let alone daily updates in the news on progress towards healing the world. Why? They should! It’s globally urgent.Oh, but presented as just a number. And numbers make us disconnect.