I need to put a vote in here for owlbears and owlcats, if only because of how excited they make my partner when encountered.

Rule 5

Really neat post, I’d not heard of a few of these (never knew libre office draw could edit pdfs!).

Couple of extra ones:

Note taking and pdf annotation: Xournal++ is amazing, it’s also great to use on larger whiteboard screens. Plug and play support for scribe tablets on both windows and Linux.

Emulation (up to ps1): Mednafen is lightweight and comes with a gui. It also supports recording, though not netplay.

Ebook management/reading: Calibre - allows easy importing and exporting of ebooks to devices, also has a great built in search letting you find DRM free versions of a book.

Yup, Google are launching their yearly attempt to convince folks YouTube premium is worth it.

Think of this time not as an annoyance, but as a time to reflect on how shitty Google has become.

Extra fact - in the USA almost all games use long weighted reels.

I believe this is by law, but may be misinformed.

Also, if you know the rng gen you can game machines: a very very clever group in Russia bought up old machines from defunct casinos, reverse engineered the games, and then developed an app that let a user photograph x number of spins to find out what the seed was for the next spin, and from there told them to bet high or low based on the upcoming game. They made millions, and farmed it out to make more. (https://www.wired.com/2017/02/russians-engineer-brilliant-slot-machine-cheat-casinos-no-fix/)

Never really worked with them (we never made them).

I think they’re lower prize threshold cat Bs.

In the UK, slot machines fall into 4 main categories. Of particular interest are category C machines, as these can remember a fixed number of previous games. I.e. the “myth” that a machine is “about to pay out” because “someone lost a lot to it” can hold for these games.

Cat A and B machines are completely random, previous games can have no impact on probabilities of winning (though pots can climb).

Online games have different rules, not always fair ones!

Oh, and ALL games (in a physical location) must (by law) show “RTP” (return to player) somewhere. It usually gets stuck it in a block of text in the manual since no-one reads them. (If it’s below 97.3% just go play roulette as it offers better returns).

Boozy Bay, it has an export industry in adventuring parties due to the booming tavern industry.

Hah, jokes on them, my university is too poor to afford copilot.

I mean, here is a thought, if an AI tool uses creative commons data, then it’s derivatives fall under creative commons. I.e. stop charging for AI tools and people will stop complaining.

The +5 charisma buff was too hard to pass up.

Operation archive the archive?

https://www.statista.com/statistics/513049/alphabet-annual-global-income/

Let’s pause a moment and just appreciate how much money Alphabet actually make net (after expenses). $73,795,000,000 last year - higher than the GDP of entire nations, in profit.

The “bad” year, 2022 that drove all this change, they only made $59,972,000,000 net. Oh how terrible (!)

5 years ago, they made $34,343,000,000 net, so they’ve more than doubled profits.

Take a moment to appreciate that, and really consider if they “need” the money.

I would say mathematics is a consequence of, or branch of philosophy in its own right. The name intuitionism derives from the source of this branch of mathematics - “2 primal intuitions”.

1. Twoity - we are able to perceived time, and are thus able to split the universe into two, three, four etc parts. Counting is not something we just learn, it is something built into us as humans.

2. Repetition - we can repeat operations and not stop, just as we can never stop counting.

From these two (heavily paraphrased) ideas we can derive all of mathematics.

The first is actually enough to give us everything up to the rationals, the second grants us the reals and beyond.

While we lose excluded middle, we gain things such as “all total real functions are uniformly continuous on the unit interval” (Brouwer), the removal of the information paradox in physics (someone used Posey’s take on intuitionism to rewrite all physics to see where it led), and the wonder of lawless sequences (objects we cannot predict entirely, but still work with).

The intuitionist is very very formal “you are either alive or not alive” is a very nice statement to make, but entirely worthless if one cannot tell which you are! Excluded middle is not universally false in intuitionism; it is true for decidable statements, of which having an apple or not does seem to fall within (though here we can question how “apple-like” must something be to be considered an apple if we wish to be peverse). However, to argue it is true for any statement means your disjunct (or) must be very weak indeed - the classical mathematician is happy with this, the intuitionist demands that a disjunct not only present two options, but provide a way of determining which if the two applies on a case to case basis (hence excluded middle applying for decidable things).

Simplifying your example of an apple, you can think of it as a Platonist just having the statement that everything is either and apple or not. Meanwhile, the Intuitionist also demands there be a guide on how to sort everything into “apple” or “not apple” before they make that statement.

Classical mathematics does also have a huge unintuitive step - mathematics must exist independently of humanity. Every theorem ever proved, and ever to be proved, exists somewhere. Where you ask? The platonic plane of ideal forms beckons, with all the madness it entails!

Pardon the slow reply!

Actually, AvA’ is an axiom or a consequence of admitting A’'=>A. It’s only a tautology if you accept this axiom. Otherwise it cannot be proven or disproven. Excluded middle is, in reality, an axiom rather than a theorem.

The question lies not in the third option, but in what it means for there to be an option. To the intuitionist, existance of a disjunct requires a construct that allocates objects to the disjunct. A disjunct is, in essence, decidable to the intuitionist.

The classical mathematician states “it’s one or the other, it is not my job to say which”.

You have an apple or you don’t, god exists or it doesn’t, you have a number greater than 0 or you don’t. Trouble is, you don’t know which, and you may never know (decidability is not a condition for classical disjuncts), and that rather defeats the purpose! Yes we can divide the universe into having an apple or not, but unless you can decide between the two, what is the point?

Ah, and therein lies the heart of the matter!

To the Platonist, the number exists in a complete state “somewhere”. From this your argument follows naturally, as we simply look at the complete number and can easily spot a non-zero digit.

To the intuitionist, the number is still being created, and thus exists only as far as it has been created. Here your argument doesn’t work since the number that exists at that point in the construction is indeterminate as we cannot survey the “whole thing”.

Both points of view are valid, my bias is to the latter - Browser’s conception of mathematics as a tool based on human perception, rather than some notion of divine truth, just felt more accurate.

Ok, so let’s start with the following number, I need you to tell me if it is greater than, or equal to, 0:

0.0000000000000000000000000000…

Do you know yet? Ok, let’s keep going:

…000000000000000000000000000000…

How about now?

Will a non-zero digit ever appear?

The Platonist (classical mathematician) would argue “we can know”, as all numbers are completed objects to them; if a non-zero digit were to turn up they’d know by some oracular power. The intuitionist argues that we can only decide when the number is complete (which it may never be, it could be 0s forever), or when a non-zero digit appears (which may or may not happen); so they must wait ever onwards to decide.

Such numbers do exist beyond me just chanting “0”.

A fun number to consider is a number whose nth decimal digit is 0 if n isn’t an odd perfect number, and 1 of it is. This number being greater than 0 is contingent upon the existance of an odd perfect number (and we still don’t know if they exist). The classical mathematician asserts we “discover mathematics”, so the question is already decided (i.e. we can definitely say it must be one or the other, but we do not know which until we find it). The intuitionist, on the other hand, sees mathematics as a series of mental constructs (i.e. we “create” mathematics), to them the question is only decided once the construct has been made. Given that some problems can be proven unsolvable (axiomatic), it isn’t too far fetched to assert some numbers contingent upon results like this may well not be 0 or >0!

It’s a really deep rabbit hole to explore, and one which has consumed a large chunk of my life XD

In classical logic, trichotomy on the reals (any given numbers is either >0, <0 or =0) is provably true; in intuitionistic logic it is probably false. Thanks to Godel’s incompleteness theorem, we’ll never know which is right!

It sounds really boring but… Reading nook - just a little spot to relax and read. Kit out the floor with pillows, the walls with shelves, and paint the ceiling to look like the sky.

I love it - functional and looks like the kind of home you can build up.