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The function f(x)=1/x is continuous, but its graph is not connected. It's an interesting one to explain to people.


You've edited your comment so many times my other reply just gets more and more off-topic lol


Wait what? I thought f(x) = 1 / x is continuous iff x != 0 since 1/0 == undefined.


Few things bother me more in life than the prevalence of Pi over Tau


I wonder, could a font have a ligature for the sequence "2π" that rendered it as τ?


Amen, brother!

(I am the author of The Tau Manifesto.)


I love you, I really do

That manifesto should be on the front page of the NY Times


How is this arts centre funded?


It's a non profit. They know how to play the donation game very well. They also offer classes and charge daily or monthly fees for general use.

The model works in a big city with lots of potential users and well-off people who are willing to donate. It would have to be modified if extended elsewhere


There are psychologists today who think that higher IQ is a cause of greater wealth and success. I wasn't referring to the original incarnation of IQ theory, which was designed to identify children who needed more attention from their teachers. It then morphed into a justification for racial discrimination. I still hear concepts like country IQ and racial IQ being brought up in conversations. Admittedly, the people talking about this are non-psychologists, but some of them appear to reference the psychology literature.


You're conflating psychologist and psychiatrists. Also, that sort of thing was used to rationalize eugenics a century ago - I'd be very interested if you could found some mainstream psychologists/psychiatrists who espouse those beliefs.

Edit: I see you added "Admittedly, the people talking about this are non-psychologists, but some of them appear to reference the psychology literature."

That's like making the argument that anti-Vaxers are good scientists as they sometimes reference the literature.


In the UK, they can encourage you to take certain kinds of medication. I've seen them get quite pushy with this. They can't force you unless you get committed.


You're still not clearly defining who "they" are - psychologist or psychiatrists?


I was referring to psychiatrists. I never claimed that psychologists could prescribe medication.


It would be nice if you pointed out your edits on your comments as you made them, and kept the original message up - you're making large claims (including that psychology is being used present day to justify racism), but you're really ruining any ability to have a dialogue if you continually edit and adjust your statements.


Psychologists can never force someone to take medication, even if that person is detained under the act. ("Sectioned". We don't use committed over here.


Again, I never said that psychologists could prescribe medication. I only talked about psychiatrists. I think I may have misread the parent post.

> ("Sectioned". We don't use committed over here.

OK


> A fractal isnt a manifold

Some are. A Koch curve for instance.


I believe you are correct. Koch curve is a continuous curve so its topological dimension would be 1 (not its fractal dimension).


I just derived the spherical law of cosines that's the foundation of this formula using quaternions and Sympy. The quaternions were modelled as 4x4 matrices.

The philosophy is that you can treat trigonometry as a triangle construction problem. You give me the specs of a triangle, and I can use physical tools like compasses, protractors and rulers to construct your triangle. This is similar to using trigonometry, except without any algebra involved, just construction tools. You can also use this philosophy to derive the algebraic formulas. When it came to formula derivation, I used the quaternions to simulate the physical construction, and I got out the formulas.


The last figure on this page http://www.vias.org/calculus/07_trigonometric_functions_01_0... really has that character (in 2D).

I wish trigonometry in secondary school had been taught more like this (geometrically) because it would have been good preparation for vector calculus, among other things.


That sounds like fun. Please drop a link if you post it.


See here: https://github.com/jkabrg/Spherical-law-of-cosines-proof-usi...

I'll provide more explanation later.


The advantage of calorie-counting is that it's quite easy - especially when you use something like My Fitness Pal. That doesn't mean it's correct, of course.

What alternative is this article advocating?


I guess lots of people do the mistake of having a too-small daily deficit while counting.

It's obviously not an exact science.

If you go with a daily reduction of 1000 kcal, then it doesn't matter if you have an error-margin of 300-500 kcal, you still lose weight.

If you only try to save 500 a day, and maybe are not too exact in your logging, you might not see an effect at all.


I only skimmed the article but it doesn't really advocate an alternative. It highlights that the person they were following "eat real food, not food ‘products’" and that weight watchers uses points instead of calories. So it doesn't seem like there is a nice actionable item that someone could take away from the article and apply to their own life.


I don't think the article really advocates any alternative, but I think things the best benefit of MyFitnessPal is to promote awareness of what you are intaking.

I have been receiving health coaching for last 4 months or so, and most important part that working for me is to be able to be conscious about food choices, and also being able to reflect what I have been eating and doing how well I'm doing with sugar, carbs, protein, fiber, etc., rather than just looking at the calories count. (and I do eat unhealthy stuff time to time, and I don't think my health coach is necessarily against that -- unless that's my regular habit, that is. It's more important to know how they balance out in the overall intake,)

It never occurred to me before I start measuring what I eat using MyFitnessPal. But now, seeing those numbers, I tend to consciously adjust my intake, for example, I will just eat 1/5 of that chips I wanted to eat, because I had bit of carbs today, etc., etc.,


Is there any way to actually read this? Pay wall.


The 'web' link worked for me.


There is no web link. It's a pay wall. Did you not get that?

[edit]

I was able to read it using the Tor Browser. There's a quota on the number of articles before it activates the pay wall.


This comment comes across as snarky.

You should be happy you're behind a computer screen.


I apologize, I did not intend any offense. What wording would you have found more appropriate?


Apologies, I guess I overreacted. I do that sometimes.


The user was referring to a hacker news feature. Under the main link, there is one titled ‘web’ that searches the web for the aeticle. This sometimes bypasses paywalls.

Commenting as I read your other comment; you may have misinterpreted OP m


outline.com/<original url>


The eigenvalues of a 2d rotation matrix are complex numbers. There's no point in trying to visualise the corresponding eigenvectors. You'll need 4 dimensions for that. (The 4 dimensions come from the fact that the eigenvectors of a 2d rotation matrix are elements of ℂ^2, which is topologically equivalent to (ℝ^2)^2, which is equiv to ℝ^4).

Personally, my "intuition" is based on analogies with non-complex eigenvectors, and experience solving eigenvector problems algebraically without using pictures.

Also, your 3d rotation example actually has three eigenvectors, two of which are complex. You've only found the one that's real.


Is there a program, free or otherwise, that lets you to do various algebraic manipulations, like:

- complete the square

- factorise something out

- expand something out

- etc

Doing that stuff by hand can get tedious.

I find that Sympy's simplify() often doesn't do what I want. WolframAlpha often understands what I want better. It seems like it would need non-trivial work on the UI front.


My go-to for these things is wolframalpha.com, mainly for ease of access, and the natural language interface means I don't have to remember any syntax. You can input queries like "complete the square ax^2 + bx + c" or "derivative of exp(x^3)" and get solutions, it's a real timesaver. Also, for vector/matrix derivatives, http://www.matrixcalculus.org/ is amazing.


Maxima (maxima.sf.net) is one way to do that (and a lot more). I even have it on my Android phone.


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