windows 10 – Does a BitLocker recovery key have any use on removable media, a.k.a ‘BitLocker to Go’, other than if you forget your password?

I understand that there are multiple reasons that a recovery key might be needed on a system partition, but why would I want the extra security risk of having a way of circumventing my password for removable media?

Why is windows asking for my recovery key?

Windows will require a BitLocker recovery key when it detects an insecure condition that may be an unauthorized attempt to access the data. This extra step is a security precaution intended to keep your data safe and secure

If I’ve understood this correctly, it only applies to fixed drives. Why not write down my password, or a reminder, rather than a key that’s impossible to remember and does the same thing?

This feels like a stupid question, but I’ve been unable to find a straightforward answer. Have I misunderstood something about how BitLocker to Go works? Does the recovery key offer any protection against the media or data being corrupted?

VeraCrypt appears to only require a rescue disk for the system partition.

ct.category theory – Magic behind idempotent-complete categories a.k.a. why (sometimes) be Karoubian is sexier than be Abelian

It is well know that Karoubian categories (also called idempotent-complete categories) are living between additive and
Abelian categories. While one of the most famous advantages to
work with abelian cetegories is that they are closed under
building kernels and cokernels of arbitrary morphism, the
Karoubian categories have a slightly weaker property that only
idempotent morphisms (i.e. $p$ with $p^2=p$) from there share
this property.

Nevertheless it seems that in diverse constructions Karoubian categories
or Karoubian envelopes of additive categories provide a more
natural setting than Abelian categories.

I hope my question not becomes too broad: What is the philosophical
meaning behind Karoubian categories or say in simpler words why in some constructions they are more prefered (e.g.
category of pure motives and in K-theory) in contrast to say
at first glance more ‘flexible’ abelian categories?

My natural guess is that if we think about the construction
of of the category of pure motives we start with the category
of smooth varieties over a base field and pass after
application of this magic Karoubian completion functor to
idempotent-complete categories. Since it’s not abelian it contains
by definition only kernel and cokernels of idempotent morphisms
but that’s all we need there to proceed the constrution.

This lead me to conjecture that the main advantage of
Karoubian categories in contrast to Abelian categories mights show when
one have to perform a construction where one starts with
a certain preadditive category but the construction requireres
a category having at least some kernels and cokernels.

Now one can pass canonically to the Karoubian completion or
extend the initial category to an Abelian category. But exactly here I see
an obstacle with the secound and at first glance more ‘natural’

Does there always a way to embedd a preadditive category in an abelian
category? If yes, seemingly the disadvantage of this approach
seems to be that this Abelian category is much harder to control,
while the Karoubian completion is constructed quite canonically and
behaves more ‘similar’ to initial preadditive category.

Questions: Is what I tried to sketch above exactly the motivation
why Karoubian categories are in some constructions more prefered
then Abelian categories?

Are there more reasons making Karoubian categories ‘interesting’.
Is there any intuition or important example one should have in
mind how to think about Karoubian categories?

optics – How can I calculate the effect of a supplementary close-up lens (a.k.a macro filter)?

A lens’s diopter is just the reciprocal of the focal length of the lens, with units of 1/(meters); equivalently, the focal length of a lens is just the reciprocal of the diopter value, in meters. So a +1 diopter corresponds to a focal length of 1 meter; +2 diopter corresponds to 0.5 m (500 mm); +10 diopter corresponds to 0.1 m (100 mm); etc.

Diopter units are particularly convenient to use when combining lenses together: their equivalent diopter value is just the sum of the individual diopters. For example, suppose a 50 mm lens has a +2 diopter close-up lens mounted on the front. The diopter value of the lens is 1/50mm = 1/0.05m = 20. So the total equivalent diopter value is 20 + 2 = 22, which corresponds to a focal length of about 0.045 m, or 45 mm.

But wait, if the diopter of the combined lens plus close-up lens is just the sum of the diopters, does that work for more than two lenses combined? Absolutely. Adding another +3 diopter to the previous combination results in a total diopter of 25, which corresponds to a focal length of 0.04 m, i.e., 40 mm.

How can I calculate its effect on close focusing distance?

Roughly speaking (see note below), the close focusing distance will be reduced according to:

xnew = xold / ( Dxold + 1) ,


  • xnew is the close-focusing distance with the close-up lens applied;
  • xold is the original close-focusing distance (without the close-up lens);
  • D is the diopter of the close-up lens.

For example, suppose a lens can focus as closely as 500 mm. With a +4 diopter close-up lens attached, the combination can now focus as close as 500 mm / (4 m-1 ∙ 0.5 m + 1) = (500/3) mm ≈ 167 mm.

Note: The reason I say “roughly speaking” is that these distances are based on distances from the center of an idealized single thin lens with negligible thickness, such that the thin lens formula can be used. Real-world optical lens elements have thickness, and of course real-world photographic lens systems consist of several individual lens elements and lots of air space in between many of them. Additionally, when talking about a camera lens’s Minimum Focus Distance (MFD), the MFD is measured from the camera’s film/sensor plane. Thus, the MFD includes the image-side focus object-side focus distances in the thin lens formula, as well as the substantial length of most of the lens assembly (which is usually not constant as a lens focuses). But the “close focus distance” discussed above is merely the mathematically-described object-distance side of the then lens. Thus, this formula is a guide to judge what diopter you might need.

Infinity focus

With a close-up lens, you will no longer be able to focus far away. The furthest you will be able to focus is simply the focal length of the close-up lens – i.e., the reciprocal of the diopter, in meters. So with a +4 diopter you cannot focus any further away than 0.25 meters (250 mm).

How much magnification can I get from the combination?

Assuming you’re working at the closest focus distance possible, both before using the close-up lens, and with the new closer focus distance with the close-up lens, then the image will be magnified (Dxold + 1) larger than it was without the close-up lens.

For example, if a lens’s closest focus distance is 500 mm, then with a +4 diopter close-up lens and focus at the new close focus distance of xnew, the image will be (4 m-1 ∙ 0.5 m + 1) = 3 times larger than without the close-up lens.

Note that the imaging system’s magnification is not 3:1. Rather, the ratio of magnification after vs. before, Mnew / Mold, is 3.

macbook pro – PROBLEMS WITH ICLOUD (aka Satan)

So, when I first started getting a little low on storage on my macbook, I set it up to automatically sync files to iCloud in order to optimize storage. However, since I’ve started working with digital audio workspaces, I been wanting to reverse this. I’ve been running into this problem with Ableton Live where recorded samples I’m using get sucked into iCloud, so that the media files are missing from the projects (i.e. they cannot be played or edited in the project anymore). This keeps happening repeatedly for projects I’m actively working on, so I want to disconnect my mac from iCloud entirely to prevent this, and instead, upload old, large files to something like Google Drive to free up space. I was told by an Apple Support employee that disconnecting from iCloud (by unchecking the box in settings which says “optimize mac Storage with iCloud”) is only recommended once you’ve backed up everything from your Mac somewhere, to ensure you don’t lose any files. So, I definitely want to do this before I mess with the iCloud sync settings.

The problem is, all the projects on my laptop that I want to back up to Google Drive are not truly on my laptop – instead I mostly just have folders full of file names, which are placeholders for the real ones that have been sucked into iCloud. This makes it difficult to upload them anywhere. Another crucial piece of information is that I only have 1-2 GB of storage left on my macbook, which prevents me from re-downloaded any complete projects folders from iCloud; I can only slowwwly download 1-5 audio files at a time, upload those few to Google Drive, delete the copies from my laptop and trash, repeat with different files (and I have thousands of audio recordings, so it’s a very tedious and frustrating process). So, to finally get to the punchline, I was wondering if anyone could offer any alternatives to my current painfully slow and annoying method of uploading stuff to Google Drive in this situation. 🙂

Side note – I’m not the most tech-savvy person, so it’s highly possible that I’ve mishandled this whole iCloud situation somehow, but it IS kind of wild that despite the absence of nearly all my projects from my laptop, its storage is always super full (between 1-2 GB remaining), mainly because of the 150 GB iCloud folder. The reason for its existence is unclear, as it appears to simply be a collection of duplicates of everything in my documents and desktop (and most half of the duplicate files in the iCloud folder are ALSO sucked into iCloud). I’m honestly a bit confused as to how using iCloud is supposed to maximize storage in the first place.

I should probably mention that besides the massive iCloud folder which I can’t seem to do anything about until I’ve disconnected from iCloud itself, I’ve scoured my laptop for duplicated files, applications I no longer use, etc, and make sure to empty my trash regularly to optimize space as much as possible despite the circumstances. I also asked Apple Support for help to make sure I wasn’t missing out on any other ways to maximize storage.

seo – Using Anchor Links aka Jump To Links with Internal Linking Strategy

Do anchor links that link to another page help or hurt SEO internal linking strategy?

For example, let’s say I have two pages:, and

And, on /subtopic-service I have anchor links like:

And, I link to that anchor like from the higher level page /services.

I know that anchor links aren’t indexed. But, will I get the same SEO benefit from an internal link with an anchor link?

dnd 5e – Does this character concept involving never taking a long rest and converting spell slots to sorcery points (aka coffeelock) violate RAW?

It seems that, technically, yes this is mostly legal by RAW except for two things. If you try to argue from RAW then you have to be aware that the RAW does not feature many of the things that the RAI take for granted. Most notably, the RAW does not explicitly permit you to take actions, bonus actions, or cast spells outside of combat nor can you actually take a short rest when not adventuring. This is all interpretation. Fairly obvious interpretation, sure, but then, so is “No you cannot stockpile a functionally infinite number of spell slots by getting less rest than normal.” Therefore, RAW you would have to do all of your conversions during combat. This doesn’t completely break the build. However, it does prevent you from stockpiling spell slots while avoiding combat.

Next, you seem to have trivialized the cost of having to use magical healing instead of natural rest. This will mean from a practical standpoint that a percentage of any spell slots you convert (probably the entire thing) will need to be reserved for healing.

You have to manage your time much more carefully. If an average combat is 5 rounds, your character is spending roughly 1 hour resting for every 30 seconds of strenuous activity (in a dungeon). However, you also have to make sure you have a solid 2 hour block of activity between every 6 hours of relative rest or you’ll trigger a long rest automatically.

Your character’s activity cycle would be completely incompatible with a normal adventuring group. You would be resting when they want to adventure and adventuring when they wanted to rest. You’d also have to travel separately to maintain your schedule.

Any of this aside, you would lose your stockpile the first time you took a long rest. A long rest per the RAW is just a long period of inactivity; it need not be willingly undertaken. Being held in a jail overnight, rendered unconscious at an inopportune time or any number of other things would wipe out your stockpile in one fell swoop. And of course, this would leave you weaker than a similar character with a different build because this one sacrificed better up-front power options in return for the ability to stockpile spells.

ASUS ROG GL553VE (aka FX53VE-MS74) External Monitor Connection(s)

When I attach a 3840×1080 monitor capable of 144Hz through HDMI, all I am getting is 60Hz.

There is a USB 3.1 Gen 1 Type-C port, but I cannot confirm that DisplayPort functionality is implemented.

Is there a way to get 144Hz signal out of the GL553VE, given that the Nvidia GeForce 1050Ti supports it?

history – Who was the owner of the first crypto exchange (aka dwdollar)?

I am researching the early history of Bitcoin. We know that (the first exchange) was created by ‘dwdollar’. Did we ever find out the real name of the owner or owners? or are these people still anonymous?

Edit: It seems his first name is Dustin. Not sure about last name.

keyboard – Can "expand selection" aka ctrl +. be used in the workbench?

Extending the selection (Ctrl +.) Is probably the most useful mathematical keyboard shortcut for me.

Is it available in Wolfram Workbench?

By naively pressing Ctrl +. does nothing and the search in the documentation for "Extend the selection" does not reveal anything.

[GET] Your First 100 Million – Dan Pena aka The 50 Billion Dollar Man | NewProxyLists

[GET] Your First 100 Million – Dan Pena aka The 50 Billion Dollar Man

For a book worth $ 1000 on Amazon, I thought I might as well share it here with the VIP Wink family

Dan Pena started his entrepreneurial journey with $ 800 which he turned around 450 million dollars after 8 years. He is now said to have created around $ 50 billion and is hosting high-end entrepreneurs and CEOs at his castle in Scotland, where he is hosting a full weekend of personal growth.

You can consult its main site here:


And an hour 40 minute and 2 hour 40 minute interview with Real London here:


Sales page:



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