davidamarquis's comments

The algorithm is very nice. But I think you should think about what it means to divide one integer by another. The quotient of that operation is an integer. The remainder is an integer.

Can you express the number in terms of the quotient and remainder?

Using this expression write an algorithm that outputs the quotient and remainder using only addition, multiplication and checking equality with integers.

I think doing this would make the algorithm seem less surprising.

Finding divisors is often hard when your number is large. It turns out the condition that a number n can be expressed as a multiple of two other numbers is equivalent to there being a number z less than n except for 1 and n-1 so that (z^2 mod n) == 1.

This condition is the basis of the Miller-Rabin primality test. Sadly its a bit hard for humans to implement this algorithm for mentally proving primality.

What are the arguments against RSA OAEP?

Is he though? He publishes frequently in a bunch of journals that I've never heard of but an actual cryptography expert would know that it is the asymptotic behaviour of an algorithm that matters.

You could write exactly the same post even if the only algorithm you had for factorization was trial division. You just would need to tweak the totally arbitrary cutoff point.

This is a recent development. Apple only started to care about iOS security around 2012 for example.

It looks like you have an incomplete understanding of the meaning of 'mislead'.

Quantum computing is an area where the hype is out of proportion to the certainty about time until its feasible. With self driving cars there are arguments about the number of decades until it is in use. With QC the uncertainty about building a quantum computer that can be used to break current RSA keys is about the order of magnitude of the number of years.

"Define a function h such that h(f(x), f(y)) is true iff x = y"

If an attacker can compute such a function then any cryptosystem would be broken because of the attack you give. The Goldwasser,Micali paper "Probabalistic Encryption" is a very important early result in cryptography about this fact.

The attack implies that no deterministic encryption scheme is secure.

"By our assumptions, the attacker knows f(1)".

There will not be a single value f(1) as secure encryption schemes cannot be deterministic.

There is nothing special about knowing one of the values of f(1) because modern cryptography assumes that the encryption algorithm is public.

Good mathematical work is rarely an all or nothing proposition. Many independent ideas are required and when the mathematician is very good it is rare that there will be many mistakes.

So even if there are issues with some aspect of the proof there is usually lots of interesting stuff that can be salvaged. The proof of Fermat's last theorem as originally given is an example. It was wrong, though it got patched later, but the original work was still very exciting I think.

Assuming that users who installed the app already understood the need to provide their location data. This allowed them to axe out the long-winded welcome flow and make the permissions request the second screen. The text was changed to say that users needed to “Enable Location Permissions”

Just so wrong.

My point: If you find a group of us to be deers because we allow ourselves to be distracted from the work we are required to do by the criticisms we have of others then you are made a deer as well by being critical of us.

I clicked one of the links http://calacanis.com/2015/07/04/the-most-important-piece-of-...

The 6th piece of wisdom this particular thought leader has for us is "NEVER GET INVOLVED IN POLITICS & NEVER BE NEGATIVE."

Which is followed immediately by this:

"The people who are killed, the deer, tend to huddle around the kitchen or go on cigarette breaks and bitch and complain about everyone and everything at the company. The tigers are too busy killing it to be bothered with such things... Deer: “Bitch bitch, moan moan, blame blame, cry cry. Tiger: “Hmmm…that’s an interesting take on things. I gotta get shit done, good luck with that.”

Apparently turning himself into a killer tiger who just fucking kills all the time has left him without a sense of irony.

> Not really, Kahneman is talking about doing better or worse than expected, not about your best or worst performance.

At a given point in time there are two quantities we need to worry about: how the teacher expects the student to perform at that point in time and the student's ability to perform at that point in time.

If the teacher is rational and has seen the student perform many times these quantities will be the same. I think the outcome is probably optimized if these quantities are the same at all times but in the real world there may large disparities in the values which can fluctuate over time.

Nevertheless, suppose it were the case that the values are always equal. Then Kahneman's hypothesis is obviously wrong. The student will perform better than expected roughly the same number of times they perform worse than expected (in the long run, obviously).

Regression to the mean exists, yes, but has no impact on the distribution of the events of being above the mean or below the mean.

I supposed that Kahneman would recognize this fact and he his reference to regression to the mean was based on a more complicated but much more realistic model where the expectation is not always aligned with reality. In such a model there must be a mechanism for relating the two quantities after each new performance/test/review.

I tried to think of how this model would work and suggested Kahneman meant that expectations were adjusted based on previous best values. I should have been clearer that other mechanisms were possible and that I was only guessing which Kahneman meant. Then I argued that based on my experience this is a poor model of how teachers punish/reward their students in general because it is unnatural and unhelpful to the task at hand. As this model is not valid his conclusion that people are incentivized to punish each other is specious.

First, the demonstration Kahneman arranged is simply a demonstration of regression to the mean and is not evidence of the validity of his hypothesis.

Is the hypothesis itself wrong? We can test the validity of the hypothesis on all people by testing it on a subset: teachers with expertise in the subject they are teaching. Kahneman hypothesis implies that such teachers reward students only when their level of achievement is higher than it has ever been in the past and punish them whenever their achievement is below their highest level of achievement.

This does not hold true in my experience of my own teachers. I was occasionally praised for doing well or punished (in some sense) for doing badly but much more often when I spoke with my teachers they remembered trends: I started bad and got better slowly, I started off well but seemed to get lazy, etc.

In my experience teaching first year math courses I would only automatically remember individual achievements if they were very surprising. For example, a student who was failing suddenly moving into the top of the class on a test.

I think people have a natural tendency to focus on these kind of outlying events and assign them special significance that they may not actually have. Although Kahneman does not mention this tendency his hypothesis suggests he also believes this.

But compared to the interesting outlying events the vast majority of student's achievements are not memorable. This means a teacher will not automatically remember them. If the teacher does not choose to remember them then they will be forgotten.

Since a teacher's capacity to remember is limited, trying to remember all student's achievements or failures was low on my priority list. Knowing a student's general trajectory lets you tailor your approach when working with them on a problem whereas individual achievements or failures are usually just noise. Other teachers I knew seemed to feel the same way.

Of course my own experience is only a data point against Kaneman's hypothesis about people in general. I am sure there could be types of teaching environments where something like what he is suggesting could be true. If the performance of the students on a particular test were tied to the teacher's compensation or the opinion of people they respect or who have power over them then I can see how a student's performance on that test would get highest priority in a teacher's mind and this could lead to reactions of the kind Kaneman describes.

I agree there is almost no content in this post. Reasonable cases could be made both for and against the point I think.

Where did you get nobility from. This isn't the author's point at all. Obviously knowledge about different areas of knowledge can be of more practical benefit at different times. The point is that in the next few years knowledge of math will become relatively more valuable and programming relatively less valuable.

Regarding the quote, it is a best a great oversimplification. Mathematicians have been interested in computation for a long time. See the Euclidean algorithm for example. Interestingly its computational complexity was worked out a hundred years before computer science was even considered a subject. Many great mathematicians like Gauss also had a keen interest in computation. A description of the fast Fourier transform was found in his notes after he died.

It is true that mathematical theorems have historically not been written from a computational point of view. But many many theorems can easily be turned into an algorithm (anything based on induction for example). Mathematics has many different subfields and the number of such constructive theorems varies based on the area. However, constructive arguments in mathematics are so pervasive that I think it is silly to even try and separate computation and mathematics as separate ways of thinking.