I distinctly remember my teachers having a debate around whether or not the functions I had programmed into my calculator were "cheating". On one hand, it was a tool and notes that I had access to my peers did not. On the other hand, I had created those tools myself, and if school was supposed to train me for the real world, wouldn't I be able to use the tools I created in the real world?
I faced a similar issue with my teachers in high school - iirc I was able to argue that by programming the formulas, I was demonstrating an understanding of them. Being able to show that understanding in our testing was the concern from my teachers’ point of view.
Wow, there were actually principles behind the rules and they bothered to reason about them. That's way different than my experience with school teachers.
Ha in my school's math department the cheating thesis won and my silly single variable CAS system (which in retrospect did nothing you couldn't do with the graph functions!) got calculator programs banned. Luckily enough my specific math teacher that year didn't care enough to enforce it and it was soon forgotten
I'll throw my hat in the ring of other "xor" tricks.
So we all know addition swap. One generalization that comes to mind is doing some other in-place transform on the two input variables. Lets keep it simple and suppose that its a linear transform. Thus the problem is to apply some matrix [[a,b],[c,d]] to two input variables [x,y] using entirely in-place operations.
We can do this by realizing that our basic operands can be expressed as matrices.
x += ky is the same as the matrix
[1, k]
[0, 1]
likewise y += kx is equiv to the lower triangular matrix
[1, 0]
[k, 1]
and lastly, the = operator is equiv to a matrix with an element on the diag.
x = k
[k ,0]
[0, 1]
y *= k
[1, 0]
[0, k]
From this point on it becomes a challenge of if you can construct any desired matrix into some combination of these available ones (spoiler, yes you can).
The next generalization one could contemplates is doing operations in place on more than 2 variables. Well, if one has already solved arbitrary 2x2 matrix operations, then that can be rigged to implement larger matrices one submatrix at a time.
The final generalization that comes to mind is what can we do with non-arithmetic operators? We've already seen an example of this with using xor-swap rather than addition-swap. But is there anything out there vaguely like xor-2x2-matrix-multiply?
I legit don't know. I have some thought, but I won't meander out loud if its not going to lead anywhere.
Something I've learned is that in a certain social strata when people do audaciously stupid, its rarely because they lack the common sense to have covered their tracks. Its because they've learned they don't have to. No one is working hard to try and catch them, and even if by some miracle someone does (and people believe them), no government or regulatory body is really interested in punishing them anyway.
This broadly goes for non-criminal acts too. Sometimes powerful people do seemingly dumb things because they are only dumb in the context of the incentive structures if one of us tried to do it. In their context, it would be stupid not to egregiously take advantage.
In my experience, people of every social strata sometimes do audaciously stupid things, and it's not because they get special treatment. It's often the people who have gotten in trouble the most that do audaciously stupid things the most frequently, despite experiencing past punishment.
Your observation matches what we would see if those people you speak of were just stupid for no reason and committed crimes that aren't caught as often. If a crime is only caught 10% of the time, they probably won't get caught the first few times. You can interpret that as them learning they can get away with it, but the person who just does stupid stuff for no reason will do the same thing, it isn't evidence one way or the other.
And they'd still be stupid the first time they committed the crime, before they've learned they can get away with it. And if they get convicted eventually, it was still stupid in the end. And if they don't get caught, we usually don't know about it, which makes it hard to argue that it's actually worth it for them to do these seemingly stupid crimes; we know of their failures but not their successes.
Well rather than our respective anecdotes, I cite page 252-253 of the Knapp Commission Report on Police Corruption in New York (1972).
>It is clear that the risks of severe punishment for corrupt behavior are slight. A dishonest policeman knows that, even if he is caught and convicted, he will probably receive a court reprimand or, at most, a fairly short jail sentence. Considering the vast sums to be made in some plainclothes squads or in narcotics enforcement, the gains from corruption seem far to outweigh the risks. Both William Phillips and Edward Droge said that they assessed the risk of meaningful punishment and determined that they had little to fear.
I've read enough reports of this nature and experienced enough regulators to be really convinced that where you see apparent stupidity you are also likely to see a table like the one on page 250 showing virtually no prosecutions prior to the Commission.
Neither Drodge nor Phillips were wrong in their calculation. I hate to say, your estimate of a 10% chance of getting caught was way too optimistic. Going by the data, it was much much lower than that.
(My axe to grind is not with the police in particular, reports on police corruption just happen to be the most available and easily understandable).
Conversely I didn’t understand incentives for junkies to steal bikes to sell those only for 10 or 20 bucks.
My incentive structure is nowhere near to theirs. It took a lot of mental effort and empathy for me to grasp what kind of environment they navigate in life to steal my bike I bought for $200.
So I also lack understanding of being a millionaire or a billionaire but I definitely lack empathy for those people.
I do love this song and I find it resonates to read the lyrics as though revolutions are censored by media (which is true). Though I found an interview with Gil Scott-Heron about the meaning of the lyrics and I find it more interesting; The revolution will not be televised because the revolution starts in your mind, at the dinner table, or reading books in the library. It won't be captured on TV because the revolution occurs when you question your own beliefs and understand something bigger.
Art in general is this way. It's no wonder the more we abstract away our lives and society (through screens, deliveries, etc) the more abstract art feels more relevant to our experience.
* The revolution won't be televised because we don't watch TV anymore (and are fragmented and increasingly don't even have those common touch points anymore).
There's a recording from the 80s where he makes the same point in the middle of reciting the poem. It's a really good version.
"A lot of times people see battles and skirmishes on TV and they say 'Ah-ha! The revolution is being televised!' Nah. The results of the revolution are being televised. The first revolution is when you change your mind, about how you look at things, and see that there might be another way to look at it that you have not been shown. What you see later on is the results of that, but the revolution, that change that takes place, will not be televised."
That's from the good old days where truth mattered. Like how many action movies are about "getting the truth out" where that act in itself brings consequences, cut, happy ending?
Compare with now: revolution may be televised, but its spread not amplified and its authenticity denied. And if you have sufficient tribalism, it will not make a dent.
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