What should a secure passphrase look like?

We all know that passwords should not only be randomly generated, but also look random. The reason is that attackers can use patterns or existing words to be able to bruteforce the passwords faster, so a randomly generated password that (by pure chance) looks like wwwtroy31 is less secure than a randomly generated password like 2ug9wf4v. The question is: should the same reasoning apply to passphrases? How? What should a secure passphrase look like? What kind of passphrases should be discarded, even if we generate them completely randomly?

Take a look at this mix of TTRPG and board game

What do you think of this experiment?

https://docs.google.com/document/d/1rkb5yVEv-75Vg3E_ruvXPuL9t26agSb5saiRrDn8UI4

”(Les combattantes) This is the game of the back alleys in the big cities, the grasslands at the outskirts of the rural areas, the field of the duel at dawn, the meetup of fighters in the park. The game of swashing blades, rivaling schools and swordplay and the bash of combatants in battle. You are the duelling gentlemen, the nobles, the privateers, the henchmen, the thugs and fighters of the streets.

This is the narrative of duelling. Duelling in the sense of swordmasters, weapon schools, sunset duelling and honor. You are a fighter with an specific style and your school. Combat is both luck and skill.

Manage your opportunities and movement and you will come out on top. Whittle down your opponent’s stamina in order to score hits, chase your opponent away from battle, knock your opponent out and win the duel.

what do infinitesimals look like?

i was looking at infinitesimals https://en.wikipedia.org/wiki/Hyperreal_number, and i have a few questions

(1) is every finite number in the nonstandards reals of the form x+epsilon, where x is a normal real number and epsilon is an infinitesimal?

(2) what does the nonstandard real line look like? it reminds me of the cantor set, because for every infinitesimal epsilon u can have another layer of infinitesimal with respect to it (epsilon^2), in a fractal fashion. is the nonstandard real line totally disconnected?

(3) what’s the point of using this anyway? it seems to be totally disconnected and doesnt seem to have anything to do with our intuition of what a continuous line is. how can you even do analysis with it? in my brief contact with intro analysis the conditions of continuity/completeness/compactness are essential, yet this nonstandard real line looks extremely pathological.

Default color profile for display and mystery profiles that look like defaults

When I go into ColorSync Utility and look under the Profiles tab in the Profiles window or when I go into System Preferences and go to the Color pane of Displays preferences, I don’t see anything that looks like a “default” profile.

There are two display profiles named “iMac” that appear in the Color pane in System Preferences that are the first ones listed in the selection box and the only ones listed if I have “Show profiles for this display only” checked. The files associated with these two profiles are stored in /Library/ColorSync/Profiles/Display and their filenames are of the form iMac-{UUID}.icc where {UUID} is a UUID with uppercase letters. The UUID for one of them is mostly zeros and it was created, or last modified, three years ago. The other one has a more random-looking UUID in the filename and it was created only a few days into this year. I am unaware of what could have created this second file; no system update was performed around that time nor was I messing with color profiles.

The two color profiles are not identical. Several fields differ between them, but these differences are almost all seemingly ordinary because they are for fields like the profiles’ creation times and their filesystem paths.

I stumbled upon these profiles while I was trying to undo a change I thought I had made to my computer’s display settings in an attempt to resolve the problem of blurry text elements on my system.

Is there a default color profile that ships with macOS or is it generated to fit the display? I don’t know much at all about “color profiles” or what they do, so much of this is beyond me. I am running El Capitan.

Nikon D500 displaying pictures that look cartoon-like

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I think I turned on a setting that makes my pictures look cartoon-like when displayed using the playback image on Nikon. Please see image below of a screen shot of what I see on the Nikon. When I download the picture, it looks normal and in focus. This picture was used taking Auto and not special settings. Please advice how to turn off this setting. Thank you!

A look at an exact smallest grammar algorithm. How do we compute running time big-O?

Pervasive are smallest grammar approximation algorithms. But rarely if ever do they talk about what would be an exact algorithm for computing smallest grammars, regardless of its efficiency.

Here I attemp to exhibit an algorithm but of course I want to make it as efficient as possible. The idea is to construct a grammar starting at the leaf production rules and constructing from them the next stage, until there’s nothing left to construct.

Let $ s$ be a string over the singleton alphabet $ \Sigma = \{a\}$ .

For instance $ s = a^6$ .

A substring $ t \leqslant s$ is repeating in $ s$ if $ t \gamma t \leqslant s$ .

A substring $ t \leqslant s$ is irreducible if it contains no repeating substrings itself.

The repeating irreducibles of length $ \geq 2$ in $ s$ are $ I = \{ a^2, a^3 \}$ . These represent all possible terminal rules that could occur in a smallest grammar of $ s$ . A terminal rule is simply a rule with no variables occuring on the right of its arrow.

Now form and keep track of the rules $ R = \{A \to a^2, B \to a^3\}$ and put $ X := \{ A, B, a\}$ . Now compute all $ xy$ such that $ x, y \in X$ and the grammar $ G = \{ S \to xy\} \cup \text{Rules}(x) \cup \text{Rules}(y)$ is irreducible and $ \overline{G} \leqslant s$ , where $ \overline{G}$ is full grammar expansion to string $ \text{Rules}(\gamma)$ is defined recursively as follows:

$ $ \text{Rules}(a) = \{\} \ \text{Rules}(uv) = \text{Rules}(u) \cup \text{Rules}(v) \ \text{Rules}(U) = \{U \to \gamma_U\} \cup \text{Rules}(\gamma_U), \ $ $ where $ u,v$ are any nonempty strings, and $ U \to \gamma_U \in R$ .

Add each such $ xy$ to $ X$ . Now keep repeating the last step (augmenting $ X$ ) until it no longer changes size. So we have for $ s = a^6$ :

$ $ X_0 = \{ A, B, a\} \ X_1 = \{A^2, Aa, aA, aB, Ba, B^2 \} \ \vdots \ X_h = \dots $ $ Notice that we didn’t add in stuff such as $ AB$ since the resulting test grammar $ G$ would be reducible since $ a^2 \leqslant a^3$ . In other words we’re constructing only irreducible grammars!

What are methods to estimate the upper bound on $ |X_h|$ ? That would give an idea of the running time.


Forgot to mention, $ t$ is a substring of the grammar $ G$ , written $ t \leqslant G$ if for some rule $ M \to \gamma_M$ in $ G$ , $ t$ is a substring of $ \gamma_M$ .

A substring $ t \leqslant G$ is repeating if it is repeating in some $ \gamma_M$ for some $ M \to \gamma_M \in G$ , or if it is a substring of at least two rules in $ G$ .


Note that smallest grammar implies irreducible grammar, but not vise versa. So we’re constructing a larger class of grammars than “just the smallest” and then checking each.

How can I inexpensively create the white backdrop look?

I’m about to do some more clothing photography, this time with the clothing flat on the floor and the camera looking straight down at the subject.

Does anyone have any tips for creating an inexpensive white backdrop for the pictures?

The local DIY store has some cheap wide roller blinds available so I was thinking about trying that out.

How to look up by “backward match” in Dictionary.app on macOS

Dictionary.app on macOS can look up words forward match now. Can we look up items by backward match in Dictionary.app?

(If I’m allowed to wish so much, I would like to do that by “middle match”, too.)

The image here is an example of forward match. If you can do backward match, you will get something magical, for example.

here is an example of forward match