lisper

51 ms·

931.
by lisper 2y ago
> There is a concrete complex number e^i: Yes, that is true, of course. But consulting a Lisp REPL merely demonstrates that it is true. It does not explain why it is true. You'd get further, pedagogically speaking, by pointing
932.
by lisper 2y ago
That's splitting a pretty fine technical hair for pedagogy at this level.
933.
by lisper 2y ago
Maybe you don't want well-defined terms in your pedagogy, but I do.
934.
by lisper 2y ago
> e is the base rate of growth shared by all continually growing processes. I don't think that's a very good explanation because all the heavy lifting is being done by the phrases "base rate" and "continually gro
935.
by lisper 2y ago
> Can't the same thing be said about using fractions on the exponent? Yes, it can. In fact, it is really useful to think of the "usual" definition of exponentiation as repeated multiplication as nothing more than a specia
936.
by lisper 2y ago
> The general differentiation of b^x, for b a constant and x the variable, is ln(x)*b^x. That's true, but it's begging the question because you can't define ln without already knowing about e. You have to go back to first
937.
by lisper 2y ago
> The "has nothing to do with exponentiating e" I would strongly disagree with. That was a bad way of phrasing it. I should have said something more along the lines of "... has nothing to do with multiplying e by itself i
938.
by lisper 2y ago
That's kind of the point. The only background knowledge you need to understand my definition is how to differentiate a polynomial. Anyone capable of understanding what it even means to find a function that is its own derivative is
939.
by lisper 2y ago
Nope. Thanks for the pointer. And thanks for pointing out CIS. I've been coding in CL since before it was standardized and I had never run across that before. But yes, one of the things I love about CL is that I can do (expt (sqrt
940.
by lisper 2y ago
Yes. Multiplying any function by a constant changes its derivative by the same constant, so for any function f, if df = f then d(Cf) = Cf. So yes, you can multiply by C without losing the interesting properties of the derivative (what
941.
by lisper 2y ago
That may be how it was arrived at historically, but it is not the best way to explain it. e arises when you ask the question: is there a function that is its own derivative? And it turns out the answer is yes. It is this infinite series:
942.
by lisper 2y ago
It turns out I was not as wrong as I thought. From the opening of the paper: "...the term halting problem , the modern formulation of the problem, as well as the common self-referential proof of its undecidability, are all, strictly
943.
by lisper 2y ago
Thanks. BTW, hats off to you for the subtlety of your pedantry. You made me realize that I was wrong by asking just the right question. Socrates would be proud.
944.
by lisper 2y ago
Yes, I think you might be right about that. FWIW, it's 4AM here and I am not firing on all cylinders. I live in the U.S. and politics is weighing heavily on my mind tonight.
945.
by lisper 2y ago
> Circular programs in Turing's language are those that return to some exact earlier state No, they aren't. They are programs that print a finite number of "symbols of the first kind" i.e. 0s and 1s. They can print
946.
by lisper 2y ago
The key is the assumption that the machine is non-circular. So there must be a state in which it prints its last symbol (can we agree to drop the "of the first kind" qualification?). After that, it never prints another symbol, s
947.
by lisper 2y ago
No. In fact, my guess is that you can prove there is no such function. But (and I confess I have not thought this all the way through so I might be wrong) while producing such a mapping would be sufficient to carry out the equivalence pro
948.
by lisper 2y ago
This is ridiculous academic click-bait. Here is a quote from Turing's 1936 paper: "If a computing machine never writes down more than a finite number of symbols of the first kind [i.e. 0 or 1], it will be called circular. Otherwi
949.
by lisper 2y ago
Maybe -i can.
950.
by lisper 2y ago
You'd be surprised at the number of things that appear to be self-evidently true that turn out to depend on tacit assumptions. For example, is 7 prime? Not if you're doing modular arithmetic.
951.
How We Shower and Do Laundry at -71°C (-95°F) in Yakutia, Siberia [video](youtube.com)
26 points by lisper 2y ago|11 comments
952.
by lisper 2y ago
> Property rights are not rights to a common resource. They can be. Native Americans considered e.g. land to be a common resource, and yet today you can own it. What is a "common resource" is a matter of social convention, no
953.
by lisper 2y ago
Thanks. I'm glad your kid is OK, and sorry that you need to deal with the added stress. Still it leaves me wondering where is the data on the kids who have this happen to them whose parents don't happen to have an epi-pen on hand
954.
by lisper 2y ago
The gulf between what the average person knows and what they would need to know in today's world to live an autonomous self-directed life with full agency, free from covert coercion by large corporate entities, is truly staggering. Ev
955.
by lisper 2y ago
OK, but surely not everyone does this? Here's the thing: if there really are kids out there who will drop dead within minutes of eating a sesame seed, surely some of them will discover this the hard way, i.e. by accidentally consumin
956.
by lisper 2y ago
Thanks.
957.
by lisper 2y ago
> If my child ingests sesame, they go into anaphylactic shock and without an epipen administered in minutes they will die. Please excuse my skepticism, I am asking this out of a genuine desire to become better informed: how can you possi
958.
by lisper 2y ago
> I think it uses Cohen's forcing You don't have to give a full proof, just an intuitive explanation of why the "obvious" arguments fail. For example, we can prove the non-emptiness of product sets for finite sets.
959.
by lisper 2y ago
To which I would add: different ways of setting it up have different consequences. The fact that this service is both reliable and free means that I have no incentive not to get my pump fixed when it fails, which makes it less likely that
960.
by lisper 2y ago
> Singapore as the benchmark for "competent local government" seems flawed. That may well be, but taking issue with the headline's factuality is different than declaring it to be nonsensical , which is what the GP was e

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