Tag: maths

Houston, we have a problem

Posted in perception, philosophy, psychology, reality, societyTagged , , , , , , , , , , Leave a comment

EDIT: Since I first posted this, I’ve discovered that computer algorithms and maths are not playing well together in the sandbox. Those naughty computer geeks are running rogue from the maths geeks.

In grade school, we typically learn a form of PEMDAS as a mnemonic heuristic for mathematical order of operations. It’s a stand-in for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This may be interpreted in different ways, but I’ve got bigger fish to fry. It turns out that many (if not most) programming languages don’t implement around a PEMDAS schema. Instead, they opt for BODMAS, where the B and O represent Brackets and Orders—analogous to Parentheses and Exponents. The important thing to note is the inversion of MD to DM, as this creates discrepancies.

And it doesn’t end here. HP calculators interject a new factor, multiplication by juxtaposition, that mathematician and YouTuber, Jenni Gorham, notates as J resulting in PEJMDAS. This juxtaposition represents the implied multiplication as exemplified by another challenge;

1 ÷ 2✓3 =

In this instance, multiplication by juxtaposition instructs us to resolve 2✓3 before performing the division. Absent the J, the calculation results in ½✓3 rather than the intended 1/(2✓3). As with this next example, simply adding parentheses fixes the problem. Here’s a link to her video:

And now we return to our originally scheduled programming…

Simplifying concepts has its place. The question is where and when. This social media war brings this back to my attention.

As depicted in the meme, there is a difference of opinion as to what the answer is to this maths problem.

6 á 2 ( 1 + 2 ) =

In grade school, children are taught some variation of PEMDAS, BOMDAS, BEDMAS, BIDMAS, or whatever. What they are not taught is that this is a regimented shortcut, but it doesn’t necessarily apply to real-world applications. The ones defending PEMDAS are those who have not taken maths beyond primary school and don’t use maths beyond some basic addition and subtraction. Luckily, the engineers and physicists who need to understand the difference, generally, do.

Mathematicians, scientists, and engineers have learned to transform the equation into the form on the left, yielding an answer of 1. If your answer is 9, you’ve been left behind.

Why is this such a big deal?

When I taught undergraduate economics, I, too, had to present simplifications of models. In practice, the approach was to tell the students that the simplification was like that in physics. At first, you assume factors like gravity and friction don’t exist—fewer variables, fewer complexities. The problem, as I discovered in my advanced studies, is that in economics you can’t actually relax the assumptions. And when you do, the models fail to function. So they only work under assumptions that cannot exist in the real world—things like infinite suppliers and demanders. Even moving from infinite to a lot, breaks the model. Economists know this, and yet they teach it anyway.

When I transitioned from undergrad to grad school, I was taken aback by the number of stated assumptions that were flat out wrong.

When I transitioned from undergrad to grad school, I was taken aback by the number of stated assumptions that were flat out wrong. Not only were these simplifications flat out wrong, but they also led to the wrong conclusion—the conclusion that aligned with the prevailing narratives.

This led me to wonder about a couple of things

Firstly, if I had graduated with an English degree and then became a PhD candidate in English, would I have also learnt it had mostly been a lie for the purpose of indoctrination?

Secondly, what other disciplines would have taught so much disinformation?

Thirdly, how many executives with degrees and finance and management only got the fake version?

Fourthly, how many executives hadn’t even gotten that? Perhaps they’d have had taken a class or two in each of finance and economics and nothing more. How many finance and economics courses does one need to take to get an MBA? This worries me greatly.

To be honest, I wonder how many other disciplines have this challenge. I’d almost expect it from so-called soft sciences, but from maths? Get outta here.

Half-life of knowledge

This also reminds me of the notion of the half-life of knowledge. What you knew as true may eventually no longer be. In this case, you were just taught a lie because it was easier to digest than the truth. In other cases, an Einstein comes along to change Newtonian physics into Oldtonian physics, or some wisenheimer like Copernicus determines that the cosmic model is heliocentric and not geocentric.

If you’ve been keeping up with my latest endeavour, you may be surprised that free will, human agency, identity, and the self are all human social constructs in need of remediation. Get ready to get out of your comfort zone or to entrench yourself in a fortress of escalating commitment.

Not Just a Number

Posted in identity, language, perception, philosophy, psychologyTagged , , , , , , , , , Leave a comment

That perception and memory work hand in hand is mostly taken for granted, but this case reminds us that this sometimes breaks down. This is not the case of the neurotypical limitations to fallible sense organs and standard cognitive boundaries and biases. This subject can’t discern the arabic numerals from 2 through 9.

To recap the study, the man can perceive 0 and 1 as per usual, but numerals 2 through 9 are not recognisable. Not even in combination, so A4 or 442 are discernible.

In a neurotypical model, a person sees an object, a 3 or a tree, and perhaps learns its common symbolic identifier—’3′, ‘three’, or ‘tree’. The next time this person encounters the object—or in this case the symbol—, say, 3, it will be recognised as such, and the person may recite the name-label of the identifier: three.

It might look like this, focusing on the numerals:

Encounter 1: 3 = X₀ (initial)
Encounter 2: 3 = X₁ ≡ X₀ (remembered)
Encounter 3: 3 = X₂ ≡ X₀ (remembered)

In the anomalous case, the subject see something more like this:

Encounter 1: 3 = X₀ (initial)
Encounter 2: 3 = Y₀ = { } (no recollection)
Encounter 3: 3 = Z₀ = { } (no recollection)

For each observation, the impression of 3 is different.

Phenomenologically, this is different to the question of whether two subjects share the same perception of, say, the colour red. Even if you perceive red as red, and another perceives red as red, as long as this relative reference persists to the subject, you can still communicate within this space. When you see a red apple, you can remark that the apple is red—the name marker—, and the same is true for the other, who can also communicate to you that the apple is indeed red because the word ‘red’ become a common index marker.

But in the anomalous case, the name marker would have little utility because ‘red’ would be generated by some conceivably unbounded stochastic function: 

Colourₓ = ƒ(x), where x is some random value at each observation

It would be impossible to communicate given this constraint.

This, as I’ve referenced, is anomalous, so most of us have a stronger coupling between perception and memory recall. Interesting to me in this instance is not how memory can be (and quite often is) corrupted, but that fundamental perception itself can be corrupted as well—and not simply through hallucination or optical illusion.