Morris comes across as pulling a Neil deGrasse Tyson stunt.
Errol Morris Refutes It Thus
21–30 of 36 posts
Re: Errol Morris Refutes It Thus
#22Earlier quoted context omitted.
I reviewed Weinberg's book and took a somewhat different stance on the issue here: https://www.chronicle.com/article/VialError/234826 Ironically, given the fact that Morris and Weinberg both prize clarity of thought, I think they are talking at cross purposes when they critique historians of science and are not properly defining their terms. Take this quote from the OP for instance: "While studying at Princeton, Morr…
Your review is a very interesting take. It reminds me of someone's observation (I forgot whose) that mathematics is often presented as a set of successful proofs and derivations, without an explanation of the motivation behind them or how they were discovered. So proof tactics may seem somewhat magical, even though they might in fact be a result of a mathematician's tinkering and blundering around, including alternat…
>An interesting example that someone gave from elementary mathematics is the derivation of the quadratic formula...
A tangential point: this is indeed a horrible way to derive the formula, for the reasons you mentioned.
If anyone is curious, here's a better way to think about it. The graph of ax² + bx + c is just the graph of ax² translated. Keeping that in mind, let's investigate.
First, consider a very easy problem: find roots of ax² = 0. The graph intersects the x-axis at x=0, done.
Now, let's shift the whole graph down by Q, and solve the problem again. The equation for that graph is ax² - Q, and it intersects the x-axis at ±√(Q/a). Still easy.
Now, let's shift the whole graph again to the right by R. The equation for that new graph is a(x-R)² - Q.
What of the roots? Oh, we don't need to do much work here! The places where the graph intersects the x axis simply shifted to the right by R. So the roots are R±√(Q/a).
So, to recap: the roots of a(x-R)² - Q = 0 are R±√(Q/a).
What if our equation is written in the form ax² + bx + c? Well, now is the time for algebra. Open up the parentheses:
a(x-R)² - Q
=a(x² - 2xR + R²) - Q
= ax² + (-2aR)x + (aR² - Q)
= ax² + bx + c
Solve the following system for Q and R:
-2aR = b
aR² - Q = c
Obtain:
R = -b/2a
Q = b²/4a - c
Now plug these Q and R into the formula we already have: R±√(Q/a) - to obtain the all-familiar result
x=(-b±√(b²-4ac))/2a
What the formula is hiding is the simple idea that the roots of a parabola are easily found if you know where the vertex is. So assume you do, and work backwards from there.
A deeper idea is solving an easier version of the problem, and then changing the problem back to the more general original question, refining the solution on each step.
And this is, in fact, how mathematics is often done.
>and that kind of thing is in fact the rule rather than the exception in many parts of math study.
There's work done to change it[1]. Note that in the argument above, I could have left out all the "work", leaving only the questions, and many people would still be able to do the work. And with the right preparation, the student would be led to ask the same questions.
Re: Errol Morris Refutes It Thus
#23Earlier quoted context omitted.
Your review is a very interesting take. It reminds me of someone's observation (I forgot whose) that mathematics is often presented as a set of successful proofs and derivations, without an explanation of the motivation behind them or how they were discovered. So proof tactics may seem somewhat magical, even though they might in fact be a result of a mathematician's tinkering and blundering around, including alternat…
>An interesting example that someone gave from elementary mathematics is the derivation of the quadratic formula... A tangential point: this is indeed a horrible way to derive the formula, for the reasons you mentioned. If anyone is curious, here's a better way to think about it. The graph of ax² + bx + c is just the graph of ax² translated. Keeping that in mind, let's investigate. First, consider a very easy problem…
Thanks! It's quite possible that my example came from Paul Lockhart or a proponent of somewhat similar ideas.
Re: Errol Morris Refutes It Thus
#24Earlier quoted context omitted.
Your review is a very interesting take. It reminds me of someone's observation (I forgot whose) that mathematics is often presented as a set of successful proofs and derivations, without an explanation of the motivation behind them or how they were discovered. So proof tactics may seem somewhat magical, even though they might in fact be a result of a mathematician's tinkering and blundering around, including alternat…
>An interesting example that someone gave from elementary mathematics is the derivation of the quadratic formula... A tangential point: this is indeed a horrible way to derive the formula, for the reasons you mentioned. If anyone is curious, here's a better way to think about it. The graph of ax² + bx + c is just the graph of ax² translated. Keeping that in mind, let's investigate. First, consider a very easy problem…
And that's just a special case of Completing the Square (but has a very handy visualization).
Re: Errol Morris Refutes It Thus
#25Earlier quoted context omitted.
Your review is a very interesting take. It reminds me of someone's observation (I forgot whose) that mathematics is often presented as a set of successful proofs and derivations, without an explanation of the motivation behind them or how they were discovered. So proof tactics may seem somewhat magical, even though they might in fact be a result of a mathematician's tinkering and blundering around, including alternat…
>An interesting example that someone gave from elementary mathematics is the derivation of the quadratic formula... A tangential point: this is indeed a horrible way to derive the formula, for the reasons you mentioned. If anyone is curious, here's a better way to think about it. The graph of ax² + bx + c is just the graph of ax² translated. Keeping that in mind, let's investigate. First, consider a very easy problem…
Personally I prefer to break things into three steps:
First put the equation into the form
x² = 2ax + b
Now complete the square:
(x – a)² = a² + b
Finally,
x = a ± √(a² + b)
Re: Errol Morris Refutes It Thus
#26Earlier quoted context omitted.
I reviewed Weinberg's book and took a somewhat different stance on the issue here: https://www.chronicle.com/article/VialError/234826 Ironically, given the fact that Morris and Weinberg both prize clarity of thought, I think they are talking at cross purposes when they critique historians of science and are not properly defining their terms. Take this quote from the OP for instance: "While studying at Princeton, Morr…
> the idea that the specific path of progress is inevitable. Seems like a straw man.
Is it?
The quoted proposition is really two rolled into one:
1. Progress is inevitable.
2. Conditional on progress occurring at all, it has to take something reasonably close to a specific path.
The first view seems to be quite widely held. I think it's false, but the second one is true. Is the version being critiqued here, the first one, second, or both?
Re: Errol Morris Refutes It Thus
#27Off-topic, but their GDPR popup just redirects me to the same popup.
Same, and I'm not even in the EU so poor targeting to begin with.
Re: Errol Morris Refutes It Thus
#28Off-topic, but their GDPR popup just redirects me to the same popup.
Yep, tried again the next day on a desktop and going to slates sight and finding the article. Guess I'm not reading this one...
Re: Errol Morris Refutes It Thus
#29"The 18th-century Irish philosopher Bishop George Berkeley concluded that, since all we know of the universe is what our senses convey to us, things in the world exist only to the extent that we perceive them." This is a mischaracterization of Berkeley's position. Berkeley did not admit even the existence of the senses, much less that they convey anything to us, nor the unstated assumption of the above description th…
Before anyone jumps into Berkelyian idealism like a conspiracy theorist into youtube, note that this whole line of thinking is fundamentally based on a genetic fallacy embed in an antiquated notion of causation.
Historically it was thought that the cause of something (the origin) must share properties with the event caused (the product). This is just a false assertion. Today we understand "emergence" in which properties arise in aggregate products that are not present in their constituent origins.
Without that every argument of the form "experience is a closed system" fails: the causal origin of experience does not "need" to be experience.
Light strikes a surface, it collides with your eye, your nervous system enters a state known as "visual perception" and that has properties not present in any prior step (ie., it feels like something). These properties emerge out of the whole interaction of the system, and are not present within any mere piece of it.
Idealism is very much an epistemological virus, a metaphysical conspiracy theory, that will quickly run a wildefire through your whole belief system with its plausible soundbites. "From experience, only experience, surely?!" No.
Berekely's Master Argument is the beginning of a line of "argument by amazement at how cool it all sounds" that ends up in Heidegger. Justified by the constant refrain that the experience is an epistemically closed system, a genetic fallacy whose plausibility is only ever achieved through rhetorically pleasing soundbites.
Re: Errol Morris Refutes It Thus
#30In what may be a case of Baader-Meinhof, I just came across the term "Whiggish" for the first time, reading Steven Weinberg's _To Explain the World_ (pretty good so far). He also has a dig at Kuhn, recounting a time when they met briefly and Kuhn gave a defense of Aristotle that he found incoherent. I'm no expert in the field of scientific thought, but my sympathies fall with Morris and Weinberg and the like. I agree…
> I agree with Weinberg that Aristotle understood physics worse than many schoolchildren do today. Which is not to say that Aristotle was stupid, but just that your knowledge is a function of the times you live in and the volume of past human thought you've had the privilege to learn from. Would physics as a discipline exist in its current form without thinkers like Aristotle? That’s the more important question for m…
The course of science is shaped by the natural world at least as much by people. It needs people with the curiosity of Aristotle, but how it proceeds depends also on what nature reveals to them, and on what they can pry from nature by using what they have learned so far. My guess is that something like our physics has emerged (or will, relatively shortly) on every world populated with intelligent beings.