I think think this must be why so many advanced level texts are couches in "introduction to..." language. Maybe it's a concession to not being able to cover every topic!
Because my own introduction was through combinatorial game theory, I always get excited to see some hackenbush diagrams and rarely do when the subject is mentioned.
Perk is... quite a thing. I think if you like programming because you like believing you have secret knowledge... go for it. Perk will scratch that itch. But I do not believe it beings you closer to the pantheon of God's. Ai n't gonna stop anyone from dancing with the Satyrs though, if that's your jam.
I have to agree -- I generally avoided Twitter/X over the past decade. I started poking around in there once in a while the last few months and everything time I'm left exasperated. 'I can't believe people believe any of this!!"
It's not a matter of a "deal" to be made or agreed to, it's a matter of paying a fair share of the cost to organize a society. When Capital gets to reap dual benefits of revenue from business prospects and lobbying government directly to set the tax rules, then it can't ALSO offload outlaying to the public good that it DEPENDS on to make a profit.
Avoiding tax through various loopholes that Capital gets a seat at the table to help craft, while benefitting from externalizing the costs to taxing labor is just corruption.
The standardized operations, e.g. multiplication or square root extraction, are precisely defined, i.e. the result is always defined exactly, by the combination of the corresponding operation with real numbers and by the rounding rule that is applied.
IEEE 754 also contains a list of operations that are recommended, but not defined by the standard, such as the exponential function and other functions where it is difficult to round exactly the result.
For the standardized operations, all the possible errors are precisely defined and they must either generate an appropriate exception or produce as result a special value that encodes the kind of error, depending on how the programmer configures the processor.
The standard is perfectly fine. The support of the standard in the popular programming languages is frequently inconvenient or only partial or even absent. For instance it may be impossible to choose to handle the errors by separate exception handlers and it may be impossible to unmask some of the exceptions that are masked by default. Or you may lack the means to control the rounding mode or to choose when to use FMA operations and when to use separate multiplications.
If you enable all the possible exceptions, including that for inexact results, the value of an expression computed with IEEE 754 operations is the same as if it were computed with real numbers, so you do not need to prove anything extra about it.
However this is seldom helpful, because most operations with FP numbers produce inexact results. If you mask only the exception for inexact results, the active rounding rule will be applied after any operation that produces an inexact result.
Then the expression where you replace the real numbers with FP numbers is equivalent with a more complex expression with real numbers that contains rounding operations besides the explicit operations.
Then you have to prove whatever properties are of interest for you when using the more complex expression, which includes rounding operations.
The main advantage of the IEEE 754 standard in comparison with the pathetic way of implementing FP operations before this standard, is that the rounding operations are defined exactly, so you can use them in a formal proof.
Before this standard, most computer makers rounded the results in whatever way happened to be cheaper to implement and there were no guarantees about which will be the result of an operation after rounding, so it was impossible to prove anything about FP expressions computed in such computers.
If you want to prove something about the computation of an expression when more exceptions are masked, not only the inexact result exception, that becomes more complex. When a CPU allows a non-standard handling of the masked exceptions, like flush-to-zero on underflow, that can break any proof.
Well... is it really? Just because someone can pump out some kind of product that someone will buy doesn't mean it's actually worth any externalized cost whatsoever.
It's one thing of we're talking food production and housing. Completely different if we're talking McDonald's happy meal toys.
Like, does the same argument apply to noise pollution? Are we alright installing a factory next to the symphony hall so long as the factory "owns" their land?
I think as our technology and understanding of the world grows we ought to change with it.
But who decides what is "worth" it and what isn't?
Driving around in an electric car "generates" carbon credits while biking or staying at home doesn't. None of these activities remove carbon from the atmosphere. It's just completely willy-nilly politics.
It would seem likely they were consumed by the proximate concerns of evading notice and making it to the plane and had no idea or thought about the dangers of being at such high altitudes.
There are enormous pressures on a new parent -- stress about getting back to a normal work routine and lack of sleep compound into a unique kind of stress and things start to slip.
For me: I decided I could just slow down a bit. Standing out isn't worth the stress. I don't want to slack, but I don't feel compelled to cram productivity into every moment.
3x more than the Marine Corps, for those at home keeping score.
A military branch (either de facto or de jure) that exists for the majority purpose to directly target, round up, and imprison or deport individuals on U.S. soil - especially with a proven record of limiting due process - should have NEVER happened. I cannot stress enough, we're a few bad days - and more and more likely 1 executive action away - from at-scale "Tree of Liberty" stuff.
We were 38 with our first. I strongly agree that is too late to have them, especially given the likelihood of birth defects. Thankfully, we avoided issues there.
A few years in and I feel "back on my feet", but it was harder for being older.
Because my own introduction was through combinatorial game theory, I always get excited to see some hackenbush diagrams and rarely do when the subject is mentioned.
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