I don't know why this was re-posted today (kind of suspicious that this floats again after 10 year just by chance) anyway, there is a full citation-heavy book by Gary Taubes about this, and one of his points was that the sugar industry paid 2 million in 1970's dollars to create the nutrition department of Harvard, which was the first nutrition department in the world. (This was to say that nutrition science itself has been corrupt since its birth).
To be true to Taubes, my memory was too approximate. The actual claim was that in 1976 Fred Stare, the director and founder (in 1942) of the Department of Nutrition of the Harvard School of Public Health was exposed by Michael Jacobson having received around 200.000 dollars in the course of the preceding 3 years from Kellogg's, Nabisco e and their foundations, after he had testified before the Congress about the virtues of cereal as a breakfast food. Apparently this discredited Stare as a scientist.
Wikipedia also states that "Kellogg's funded $2 million to set up the Nutrition Foundation at Harvard. The foundation was independent of the university and published a journal Nutrition Reviews that Stare edited for 25 years." But I cannot find this is Taubes's book.
The author did not see the large, outsized, springs that keep the cabin insulated from both the road _and_ the engine.
What was wrong in this design was just that the technology to keep the heavy, vibrating, motor sufficiently insulted from both road and passengers was not available (mainly inflatable tires). Otherwise it was perfectly reasonable, even commendale, because it tried to make-do with what was available.
Maybe the designer can be critizised for not seeing that a wooden frame was not strong enough to hold a steam engine, and maybe that there was no point in making the frame as light as possible when you have a steam engine to push it, but, you know, you learn this by doing.
I see the horseless carriage as part of the evolutionary product journey to what is now known as the car, from the horse-drawn carriage to the horseless carriage, to early automobiles, to now.
I would take your statement further than unfair and say the analogy is inaccurate and confused about how products evolve over time.
The article itself shows only an incremental improvement on the UI by exposing a system prompt, rather than reaching for the modern car from the era of the first horseless carriages.
Thank you for pointing this out; though the article's underlying message is relatable and well-formed, this "laughably obvious" straw man undermined some of its credibility.
The illustration of the Newton method is wrong, isn't it? The approximating second order polynomials that were drawn are not really graphs of second order polynomials, they are not even functions... those are parables in the 2D plane, but Newton's method won't work like that... Besides, the convexity of the target function looks negative near to the first guess, the Newton method shall probably miserably fail here
Perhaps the graphics designer didn't get the memo. You can see in the panels that it's the same parabola, they've just rotated it in the first panels so it seems to fit the shape of the local curve "better".
For late arrivals to this thread: note that the illustration being discussed has been updated (see the Wayback Machine for the old version). The new version probably still does not show the best second-order approximations, but the obvious qualitative errors have been corrected.
I'm not following your objection. To my eye those approximation graphs are indeed 2nd order functions in the 2d plane. But they are perhaps not parabolic for lack of symmetry?
They look symmetric to me, but that's not point anyway, I guess they are parables, only they are rotated, their axis is not parallel to the y axis.
If those are 2nd order functions in the 2d plane, then we don't agree on terminology.
The reason why I feel an expert is that it is clear at first sight to me that if you really implement the Newton method in that situation, the approximating functions that you will get are totally different from those that were drawn in the illustration.
The third parable from the left on the lower left figure, is definitely not a second order approximation to the target function: the convexity is reversed!
Well, now that you mention it, even the first one is on the wrong side of the graph. The second derivative is apparently (to my eyes) negative there, so the approximating parabola should be turning downwards. Whichever the sign, its value is close to zero anyways, the approximation would look very flat there.
Anyways, it's a little graph to illustrate the idea of a second order approximation, I think it does the job.
When you say they are not even functions, are you saying because they are not everywhere bijective? Because they look like rotated parabolas to me which means they will have continuous first and second derivatives which is (I think) all you need for Newton’s method isn’t it?
You are thinking of those parables as parametric curves, I guess, but Newton's method is about approximating an arbitrary function by its Taylor expansion truncated to the second degree, which is a polynomial function of second degree. The graphs of these functions can be thought as parametric curves, but (my point is also) these are not those that were drawn in the illustration.
I think the person meant that, to a single x, they map more than one value. A function needs to have at most one image to the antecedent. In other words, it can't have "vertical stretches". This is different from bijectivity (specifically, injectivity here) which asks that two different x values never map to the same y.
At first I thought you were not getting it, but, thinking it through, I now think the real problem is that the article gave us the averages (600, 701, 5000) without giving the standard deviations and nobody is outraged!
The combined result of the three experiments can be either surprising or absolutely obvious: if the standard deviation of each of the three experiments was around 1 cm, it would be troubling, if it was 100 cm, it would be troublesome yet, but if the standard deviation is 5000 cm, there would be nothing wrong in what happened.
> without giving the standard deviations and nobody is outraged!
I agree with that! I was just swallowing my outrage :D
> if the standard deviation of each of the three experiments was around 1 cm, it would be troubling
That would be very curious though! These are animals not robots :D The only way I could imagine them to average that small standard deviation in the distance moved if we paralyse (or almost paralyse) them.
"By learning how the Shire worked, we can start to understand how our own past worked, in all its complexity and contradictions."
Sorry but this is totally preposterous. Why should we look at our past through a fictional creation of one author? Why don't we go directly to the sources that that same author had? Makes much more sense.
"Premodern agriculture was characterized primarily as being low-surplus and high-labor, it takes a lot of people a lot of time to produce enough food for everyone to eat, and there’s rarely much left over."
This i contentious, I have actually read scholars that argue the opposite.
>This i contentious, I have actually read scholars that argue the opposite.
It is far from contentious, you are probably mixing up "premodern agriculture" with "pre-agriculture". Furthermore, as detailed in an article [1] referenced (and linked to) by this post, you are probably mixing up the labor paid as rent vs the whole of the labor required to survive
