You're taking my analogy too far. Learning isn't your ability to exercise intelligence. It's simply the acquisition of knowledge or skills usually through study or training. You're going to have to provide an argument or a source to back up the claim that intelligence is innate and that it can't be changed by adjusting our behavior. You're going to have to show that intelligence is nearly 100% determined by genetics. Those are the types of claims that eugenicists make regarding intelligence by the way, and I'm pretty sure that would make you uncomfortable given your other comment on IQ tests.
CompassRed
joined 2 years ago
I don't see how this could be true. It would be analogous to observing a species of bone-thin weaklings that becomes interested in body building over the course of a few hundred years, gaining more muscle mass on average with each passing year, and making the claim that the strength of this species has not changed. Maybe if one of the early weaklings decided to take up their own interest in body building, they may have reached a similar strength to that of their descendants (though even that is debatable since that specific individual wouldn't have access to all the training techniques and diets developed over the course of its species' future); however, it seems like an awkward interpretation to say therefore the strength of the species has not changed.
This is similar to the situation we find ourselves regarding intelligence in the human species. Humans gain intelligence by exercising their brains and engaging in mental activity, and humans today are far more occupied by these activities than our ancestors were. This, in my view, makes it accurate to claim that human intelligence has changed significantly since the advent of religion. Individual capacity for intelligence may not have changed much, but the intelligence of humans as a whole has changed.
Note that my argument does not conclude that human knowledge or understanding has changed over time. These attributes certainly have changed - I'm sure not many would doubt that. It also doesn't conclude that every modern human is more intelligent than every ancient human. Instead, it concludes that human intelligence as a whole has changed as a result of changes in our culture that influence us to spend more time training our intelligence than our ancestors.
You have the spirit of things right, but the details are far more interesting than you might expect.
For example, there are numbers past infinity. The best way (imo) to interpret the symbol ∞ is as the gap in the surreal numbers that separates all infinite surreal numbers from all finite surreal numbers. If we use this definition of ∞, then there are numbers greater than ∞. For example, every infinite surreal number is greater than ∞ by the definition of ∞. Furthermore, ω > ∞, where ω is the first infinite ordinal number. This ordering is derived from the embedding of the ordinal numbers within the surreal numbers.
Additionally, as a classical ordinal number, ω doesn't behave the way you'd expect it to. For example, we have that 1+ω=ω, but ω+1>ω. This of course implies that 1+ω≠ω+1, which isn't how finite numbers behave, but it isn't a contradiction - it's an observation that addition of classical ordinals isn't always commutative. It can be made commutative by redefining the sum of two ordinals, a and b, to be the max of a+b and b+a. This definition is required to produce the embedding of the ordinals in the surreal numbers mentioned above (there is a similar adjustment to the definition of ordinal multiplication that is also required).
Note that infinite cardinal numbers do behave the way you expect. The smallest infinite cardinal number, ℵ₀, has the property that ℵ₀+1=ℵ₀=1+ℵ₀. For completeness sake, returning to the realm of surreal numbers, addition behaves differently than both the cardinal numbers and the ordinal numbers. As a surreal number, we have ω+1=1+ω>ω, which is the familiar way that finite numbers behave.
What's interesting about the convention of using ∞ to represent the gap between finite and infinite surreal numbers is that it renders expressions like ∞+1, 2∞, and ∞² completely meaningless as ∞ isn't itself a surreal number - it's a gap. I think this is a good convention since we have seen that the meaning of an addition involving infinite numbers depends on what type of infinity is under consideration. It also lends truth to the statement, "∞ is not a number - it is a concept," while simultaneously allowing us to make true expressions involving ∞ such as ω>∞. Lastly, it also meshes well with the standard notation of taking limits at infinity.
My superiority complex is stronger than your inferiority complex.
I don't know the reason. I think not having the extra blank lines would be better, but it works just fine as is - even the post admits this much. That's why it's an enhancement. It's possible for software to be functional and consistent and still have room for improvement - that doesn't mean there is a bug.
My point is that someone made the decision for it to do that and that the software works just fine as is. It's not a bug, it's just a weird quirk. The fact that they made the enhancement you requested doesn't make the old behavior buggy. Your post title said "it's not a bug, it's a feature!", but the behavior you reported is not accurately classified as a bug.
It's not a bug just because the software doesn't conform to your personal preferences. You're asking for what would be considered an enhancement - not a bug fix.
It depends. If the variable names are arbitrary, then a map is best. If the variable names are just x_1, x_2, x_3, ..., x_n, then a list or dynamic array would be more natural. If n is constant, then a vector or static array is even better.
I don't recall any socialized courier or food delivery services.
As I already mentioned, I'm not talking about situations where your windshield is suddenly obstructed since that situation is especially rare, so if you can see clearly enough to drive safely in the first place, then you can see clearly enough to evaluate your surroundings.
It seems obvious to me that spraying your windshield with soap obstructs your view for a moment, but I'll admit that the occlusion is likely variable depending on the make and model.
I stand by the claim that it is safer to not use your wiper fluid while moving when possible. If you disagree, that's okay. It's a pretty minor point - there are many other driving habits that are far worse in my opinion.
The major determining factor in the time it takes you to get through the light is the number of cars ahead of you, not the amount of room you have for a run-up. What you're talking about might save you a quarter second at the end of the day, but it more likely to not save any time at all and it unnecessarily contributes to traffic by reducing the effective carrying capacity of the road. There are also situations where hanging back can block a turn onto a minor road or into a parking lot and moving forward may let a person behind you turn off the road thus alleviating traffic. Ultimately, there is nothing you can do to make the person in front of you go faster, so just pull up as far as you safely can to make room for other people to join the queue or get around you.
I'm not talking about either of these things. I have already stated that I'm not referring to knowledge. Additionally, I do not agree that intelligence is merely the ability to acquire knowledge. Intelligence is famously difficult to define - but I'm working with a definition akin to a capacity for problem solving and pattern recognition. If we can't see eye to eye there, then we're clearly talking past each other.
Thanks for the interesting conversation. I wish you well.