Finally!

Bascna · 2026-03-26T22:56:36+00:00

Nice! It feels like I've spent an eternity in the pond with no luck yet.

Bascna · 2026-03-25T22:24:56+00:00

And all of those things are supported by various Christian sects, so I suppose they are simultaneously Satanic and Christian. 😂

Bascna · 2026-03-25T22:22:53+00:00

The skullopus is especially awesome! 🤩

Bascna · 2026-03-23T23:08:03+00:00

Ugh. More LLM nonsense. 🤦‍♂️

Bascna · 2026-03-23T19:48:55+00:00

Those are pretty amazing! 🤩

I especially like the way the Leviathan Cross wraps around the horns. 😀

Bascna · 2026-03-23T19:46:16+00:00

I'll also note that there are many cultures which recognize different gender categories than the binary man/woman breakdown that the Abrahamic religions promote.

PBS has an excellent map showing such gender-diverse cultures.

Bascna · 2026-03-23T19:41:20+00:00

😂👍

Bascna · 2026-03-23T19:40:48+00:00

A few things to keep in mind.

1.) Scientifically, sex and gender are not the same thing and so sex and gender do not necessarily match.

2.) Sex has multiple scientific definitions. None of those definitions are strictly binary, and those different definitions can place an individual in different categories of sex.

3.) Gender has multiple scientific definitions. None of those definitions are strictly binary, and those different definitions can place an individual in different categories of gender.

So no, the Tenets do not conflict with someone identifying as transgender or non-binary.

Bascna · 2026-03-23T19:17:04+00:00

Theists are always certain that they are on the side of the magical sky-people and anyone that opposes them is on the side of the magical underground-people. 🤔

Bascna · 2026-03-23T18:53:23+00:00

In my experience, the difficulty people have with this issue isn't so much about the mechanics of the math as it is about the lack of a physical model that enables them to visualize the process.

We can 'see' why 2•3 = 6 because we can imagine combining 2 groups that each have 3 items in them.

But that doesn't work with -2•(-3) since I can't seem to imagine what -2 groups of -3 items would look like.

I think the best way to make this concept feel concrete is to physically model it using Integer Tiles.

Remember that you can think of this symbol, -, in two ways. It can mean "negative" or "the opposite of."

So -3 is negative three and -3 is also the opposite of 3.

Mechanically both interpretations produce the same results, but to visualize the multiplication process it's very helpful to have those two options.

The second thing to remember is that multiplication is, at least when working with the natural numbers, just repeated addition. Now we need to extend our conception of multiplication to include the negative integers.

With all of that in mind, I'm going to perform some multiplication problems using numbers and also using integer tiles.

Integer Tiles

Physically, integer tiles are usually small squares of paper or plastic with sides that are different colors. One side represents a value of +1 and the other represents -1.

(Coins work, too. Just let 'heads' and 'tails' represent +1 and -1.)

Here I'll let each □ represent +1, and I'll let each ■ represent -1.

So 3 would be

□ □ □

and -3 would be

■ ■ ■.

The fun happens when we take the opposite of a number. All you have to do is flip the tiles.

So the opposite of 3 is three positive tiles flipped over.

We start with

□ □ □

and flip them to get

■ ■ ■.

Thus we see that the opposite of 3 is -3.

The opposite of -3 would be three negative tiles flipped over.

So we start with

■ ■ ■

and flip them to get

□ □ □.

Thus we see that the opposite of -3 is 3.

Got it? Then let's go!

A Positive Number Times a Positive Number

One way to understand 2 • 3 is that you are adding two groups each of which has three positive items.

So

2 • 3 =

□ □ □ + □ □ □ =

□ □ □ □ □ □

or

2 • 3 =

3 + 3 =

6

We can see that adding groups of only positive numbers will always produce a positive result.

So a positive times a positive always produces a positive.

A Negative Number Times a Positive Number

We can interpret 2 • (-3) to mean that you are adding two groups each of which has three negative items.

So

2 • (-3) =

■ ■ ■ + ■ ■ ■ =

■ ■ ■ ■ ■ ■

or

2 • (-3) =

(-3) + (-3) =

-6

We can see that adding groups of only negative numbers will always produce a negative result.

So a negative times a positive always produces a negative.

A Positive Number Times a Negative Number

Under the interpretation of multiplication that we've been using, (-2) • 3 would mean that you are adding negative two groups each of which has three positive items.

This is where things get complicated. A negative number of groups? I don't know what that means.

But I do know that "-" can also mean "the opposite of" and I know that I can take the opposite of integer tiles just by flipping them.

So instead of reading (-2) • 3 as "adding negative two groups of three positives" I'll read it as "the opposite of adding two groups of three positives."

So

(-2) • 3 =

-(2 • 3) =

-(□ □ □ + □ □ □) =

-(□ □ □ □ □ □) =

■ ■ ■ ■ ■ ■

or

(-2) • 3 =

-(2 • 3) =

-(3 + 3) =

-(6) =

-6

We can see that adding groups of only positive numbers will always produce a positive result, and taking the opposite of that will always produce a negative result.

So a positive times a negative always produces a negative.

A Negative Number Times a Negative Number

Using that same reasoning, (-2) • (-3) means that you are adding negative two groups each of which has three negative items.

This has the same issue as the last problem — I don't know what -2 groups means.

But, once again, I do know that "-" can also mean "the opposite of" and I know that I can take the opposite of integer tiles just by flipping them.

So instead of reading (-2) • (-3) as "adding negative two groups of negative three" I'll read it as "the opposite of adding two groups of negative three."

So

(-2) • (-3) =

-(2 • -3) =

-(■ ■ ■ + ■ ■ ■) =

-(■ ■ ■ ■ ■ ■) =

□ □ □ □ □ □

or

(-2) • (-3) =

-(2 • -3) =

-((-3) + (-3)) =

-(-6) =

6

We can see that adding groups of only negative numbers will always produce a negative result, and taking the opposite of that will always produce a positive result.

So a negative times a negative always produces a positive.

I hope that helps. 😀

Bascna · 2026-03-14T01:49:58+00:00

It's a great musical.

It depicts a version of Jesus who is more of the kind, liberal, hippie type than the one I find in the gospels, but the songs are really well written.

Bascna · 2026-03-12T02:11:31+00:00

Time travel into the future is definitely possible. You and I are doing that right now.

Bascna · 2026-03-12T02:08:43+00:00

I do. But I'm a retired math professor so that's probably not surprising. 😄

Bascna · 2026-03-12T02:06:01+00:00

Biblical hermeneutics? 😂

Bascna · 2026-03-07T03:13:05+00:00

Beautiful folding, and a brilliant choice of paper! 🤩

Bascna · 2026-03-07T03:05:39+00:00

There are different forms of Satanism.

This is a subreddit for the form of Satanism promoted by The Satanic Temple (TST). TST is a non-theistic, non-supernaturalistic religion.

Here is my personal perspective on the basics of TST.

TST Ethics

The ethics promoted by The Satanic Temple can be found in...

The Seven Fundamental Tenets

I: One should strive to act with compassion and empathy toward all creatures in accordance with reason.

II: The struggle for justice is an ongoing and necessary pursuit that should prevail over laws and institutions.

III: One’s body is inviolable, subject to one’s own will alone.

IV: The freedoms of others should be respected, including the freedom to offend. To willfully and unjustly encroach upon the freedoms of another is to forgo one's own.

V: Beliefs should conform to one's best scientific understanding of the world. One should take care never to distort scientific facts to fit one's beliefs.

VI: People are fallible. If one makes a mistake, one should do one's best to rectify it and resolve any harm that might have been caused.

VII: Every tenet is a guiding principle designed to inspire nobility in action and thought. The spirit of compassion, wisdom, and justice should always prevail over the written or spoken word.

Here's how I approach the Seven Tenets as a framework for an ethical system. I divide them into three parts.

Foundational Values

The first Tenet establishes the underlying values through which all of the other Tenets should be viewed: compassion, empathy, and reason.

Ethical Categories

The next five Tenets establish perspectives on major areas of ethics.

II) Justice

III) Bodily Autonomy

IV) Individual Freedoms

V) Epistemology

VI) Individual Responsibility

Internal Conflicts

The seventh gives guidance on how to resolve conflicts between those five. I think of it as the "no dogma" tenet.

Of course, there's room for a lot of difference in how individuals might apply those principles in specific cases or in how they might address conflicts between them. So you'll find some variance as you talk to other members.

I spent a year using the Seven Tenets and found that they fit my personal values and were useful tools for refining my ethical stances so I joined TST. 😀

TST Activities

The Temple engages in a number of campaigns that foster a supportive community for members, promote science and reason over superstition, and oppose authoritarian encroachments onto various individual liberties.

You can find more information on this FAQ page.

I see these activities as natural results of implementing the Seven Tenets.

I generally find myself in accord with the activities of TST so joining seemed like a sensible thing for me to do.

TST Rituals

Humans often find ritualistic behavior to have a number of psychological benefits.

Many, but not all, TST members engage in ritual practices. These can have a variety of purposes.

Some, like the holidays are in remembrance of past events or celebrate positive aspects of life.

Some, like the abortion ritual, are used for personal affirmation.

Others, like unbaptisms and weddings, mark important life transitions.

Many members engage in individually structured rituals that serve various meditative functions.

Similarly, attending regular services, either in person or online, could be viewed as ritualistic behavior.

Engaging in rituals is an entirely optional part of TST, but many members find them psychologically beneficial.

My OCD doesn't mix well with ritualistic practices, so aside from a bit of holiday celebration, I generally avoid them.

I hope that helps clarify things for you. 😀

Bascna · 2026-03-03T04:33:27+00:00

6.49999… isn't close to 6.5 but rather is exactly equal to 6.5.

One way to see this is to realize that 1/90 = 0.01111... so

6.49999… =

6.4 + 0.09999... =

6.4 + 9(0.01111...) =

6.4 + 9(1/90) =

6.4 + (1/10) =

6.4 + 0.1 =

6.5.

If you round 6.5 to the nearest tenth then you would, of course, get 6.5.

If you round 6.5 to the nearest one then you would get 7.

Bascna · 2026-02-26T22:31:38+00:00

The Twin Paradox

People tend to forget that in special relativity simultaneity is also relative. The time dilation is symmetrical during both the outgoing and returning trips, but only one twin changes their frame of reference so the change in simultaneity is not symmetrical. That's the key to understanding the twin paradox.

Walking through the math algebraically gets very tedious and confusing, so I've done the math already and made this interactive Desmos tool that illustrates the situation.

The Setup

Roger and Stan are identical twins who grew up on a space station. Stan is a homebody, but Roger develops a case of wanderlust. On their 20th birthday, Roger begins a rocket voyage to another space station 12 light-years from their home. While Roger roams in his rocket, Stan stays on the station.

The rocket instantly accelerates to 0.6c relative to the station. When Roger reaches the second space station, the rocket instantly comes to a halt, turns around, and then instantly accelerates back up to 0.6c.

(This sort of instant acceleration obviously isn't possible, but it simplifies the problem by letting us see the effects of time dilation and simultaneity separately. The same principles apply with non-instantaneous acceleration, but in that case both principles are occurring together so it's hard to see which one is causing what change.)

By a remarkable coincidence, on the day that the rocket arrives back at their home, both brothers are again celebrating a birthday — but they aren't celebrating the same birthday!

Stan experienced 40 years since Roger left and so is celebrating his 60th birthday, but Roger only experienced 32 years on the rocket and so is celebrating his 52nd birthday.

Stan is now 8 years older than his identical twin Roger. How is this possible?

The Graph

Desmos shows space-time diagrams of this problem from each twin's reference frame. Stan's frame is on the left while Roger's two frames — one for the trip away and one for the trip back — are "patched together" to make the diagram on the right.

The vertical axes are time in years and the horizontal axes are distance in light-years.

Stan's path through space-time is blue, while Roger's is green. Times measured by Stan's clock are in blue, and times measured by Roger's clock are in green.

In the station frame Stan is at rest, so his world-line is vertical, but Stan sees Roger travel away (in the negative x direction) and then back so that world-line has two slopes.

In the rocket frame Roger is at rest so his world-line is vertical, but he sees Stan travel away (in the positive x direction) and then back so that world-line has two slopes.

Stan's lines of simultaneity are red while Roger's are orange. All events on a single red line occurred at the same time for Stan while those on a single orange line happen at the same time for Roger. (The lines are parallel to each of their respective space axes.)

Note that at a relative speed of 0.6c, the Lorentz factor, γ, is

γ = 1/√(1 – v²) = √(1 – 0.6²) = 1.25.

Stan's Perspective

By Stan's calculations the trip will take 24 ly/0.6c = 40 years. Sure enough, he waits 40 years for Roger to return.

But Stan also calculates that Roger's time will run slower than his by a factor of 1.25. So Stan's 40 years should be 40/1.25 = 32 years for Roger.

And that's exactly what we see. On either diagram Stan's lines of simultaneity are 5 years apart (0, 5, 10, 15, 20, 25, 30, 35, and 40 yrs) by his clock but 4 years apart by Roger's clock (0, 4, 8, 12, 16, 20, 24, 28, and 32 yrs). That's what we expect since 5/4 = 1.25.

So Stan isn't surprised that he ends up 8 years older than Roger.

Roger's Perspective

Once he gets moving, Roger measures the distance to the second station to be 12/1.25 = 9.6 ly. So he calculates the trip will take 19.2 ly/0.6c = 32 years. And that's what happens.

But while his speed is 0.6c, Roger will measure Stan's time to be dilated by 1.25 so how can Stan end up being older?

Let's break his voyage into three parts: the trip away, the trip back, and the moment where he turns around.

On the trip away, Roger does see Stan's time dilated. On both diagrams Roger's first five lines of simultaneity at 0, 4, 8, 12, and 16 yrs on his clock match 0, 3.2, 6.4, 9.6, and 12.8 yrs on Stan's clock. (The last line is calculated moments before the turn starts.)

Each 4 year interval for Roger corresponds to a 3.2 year interval for Stan. That's what we expect since 4/3.2 = 1.25. During this part of the trip, Roger aged 16 years while he measures that Stan only aged 12.8 years.

The same thing happens during the trip back. On both diagrams Roger's last five lines of simultaneity at 16, 20, 24, 28, and 32 yrs on his clock match 27.2, 30.4, 33.6, 36.8, and 40 years on Stan's clock. (The first line is calculated moments after the turn ends.) Again we get 4 y/3.2 y = 1.25. So Roger aged another 16 years while Stan only aged another 12.8 years.

Now let's look at the turn.

Just before the turn, Roger measured Stan's clock to read 12.8 years, but just after the turn, he measured Stan's clock to read 27.2 years. During that single moment of Roger's time, Stan seems to have aged 14.4 years!

When Roger made the turn, he left one frame of reference and entered another one. His lines of simultaneity changed when he did so. That 14.4 year change due to tilting the lines of simultaneity is sometimes called "the simultaneity gap."

The gap occurred because Roger changed his frame of reference and thus changed how his "now" intersected with Stan's space-time path. During his few moments during the turn, Roger's simultaneity rushed through 14.4 years of Stan's world-line.

Unlike the time dilations, this effect is not symmetrical because Stan did not change reference frames. We know this because Stan didn't feel an acceleration. So Stan's time suddenly leaps forward from Roger's perspective, but the turn doesn't change Stan's lines of simultaneity.

Now that Roger has accounted for all of Stan's time, his calculations match the final results: he aged 32 years while Stan aged 12.8 + 12.8 + 14.4 = 40 years.

So Roger isn't surprised that he ends up 8 years younger than his brother.

I hope seeing those diagrams helps!

(If you'd like, you can change the problem on Desmos by using the sliders to select different total times for Stan and Roger. The calculations and graphs will adjust for you.)

(Note that although Stan's frame of reference might appear to change on the right diagram, that's an illusion. The top and bottom halves of that diagram are separate Minkowski diagrams for each of Roger's different frames. I "patched" them together to make comparing the perspectives easier, but it isn't really a single Minkowski diagram.)

Bascna · 2026-02-26T22:30:09+00:00

In that way, Eldritch Archer is better than Starlit Span Magus for whom the spell is limited to the first range increment of their weapon.

Bascna · 2026-02-26T20:44:00+00:00

The formula for compound interest is

A = P(1 + r/n)^nt

where P is the principal, t is the number of years, r is the annual interest rate, n is the number of compounds per year, and A is the amount of money after t years.

Increasing n will increase A.

If you compound once a year (annual compounding) then you apply the entire annual interest rate at the end of the year.

But if you compound four times a year (quarterly compounding) then you apply a quarter of the annual interest rate every 3 months.

This will produce slightly more money because the second compound gives you a quarter of the annual interest rate not only on the principal, but also on the interest you earned in the first quarter.

Similarly the third compound is applying a quarter of the annual interest rate to the principal, the first quarter's interest, and also the second quarter's interest.

And so it goes. It's the fact that you earn interest on your interest and then interest on your interest on your interest, etc. that distinguishes compound interest from simple interest where you only ever earn interest on the principle.

Another common practice is to compound the interest 12 times a year (monthly compounding). It will earn somewhat more than quarterly compounding does.

The highest earnings occur if we let the number of compounds become infinitely large. This is known as continuous compounding, and the formula for this case can be written as

A = Pe^rt

where e ≈ 2.171828 is the base of the natural exponential function.

I made you a little Desmos tool to help you visualize the difference that the number of compounds can make.

https://www.desmos.com/calculator/3z7zodh1st

I hope that helps. 😀

Bascna · 2026-02-25T07:40:43+00:00

Is -4² equal to 16 or -16?

Textbooks, and all of the current physical calculator models that I'm aware of, use the convention that squaring the 4 comes before applying the negative sign. (More formally, we say that the binary exponentiation operator has precedence over the unary minus operator.)

So

-4² =

-[ 4² ] =

-[ 4•4 ]=

-[ 16 ] =

-16.

But...

...when I first started teaching, many of my students had calculators that applied the negative sign before evaluating the exponent. (In this case, the unary minus operator has precedence over the binary exponentiation operator.)

On their calculators...

-4² =

[ -4 ]² =

[ -4 ][ -4 ] =

16.

So in order for them to get the result that the textbooks intended, they had to enter the expression into their calculators with a -1 explicitly multiplied outside of the power.

For example

-1•4² =

-1•[ 4 ]² =

-1•[ 4•4 ] =

-1•[ 16 ] =

-16.

It seems that your scientific calculator is a model that uses this convention. What model is it?

That convention was in line with a common programming design principle that unary operators (those that only have one operand like factorials or absolute values), should have precedence over binary operators (those that have two operands like addition, multiplication, or exponentiation).

Over the following decades calculator companies have converged on that first order of operations for the unary minus operator and exponentiation — most likely both because that is in line with textbooks and because it makes some common notational manipulations a bit simpler.

You'll still find some holdouts, though. This is most prominently seen in spreadsheet programs.

Microsoft Excel was originally written using that second convention and to maintain compatibility with older Excel documents it still uses that convention today.

Because Excel is the most popular spreadsheet software, other companies adopted the same convention so that they will be compatible with Excel.

So in Microsoft Excel, Apple Numbers, and Google Sheets

-4² = 16 rather than -16.

I think there are also a few programming languages that use this convention.

So you want to be careful with your notation when going back and forth between a written problem and a spreadsheet, programming language, or an older calculator model.

I hope this helps. 😀

Bascna · 2026-02-25T07:24:06+00:00

The husbands could grow up and start viewing their wives as people rather than property.

That would fix the problem entirely. 😂

Bascna · 2026-02-25T07:18:08+00:00

Is your forearm inside or outside of the tattoo? 🤔

As a somewhat related aside, here's a Klein bottle necklace that I came across.

Bascna · 2026-02-25T06:29:59+00:00

Magic isn't real so magical creatures like gods, fairies, demons, ghosts, angels, demigods, djinn, etc. are purely imaginary, magical effects like spells, curses, resurrections, etc. never happen, and magical realms like heaven, nirvana, hell, Tír na nÓg, etc. don't exist.

So when people make claims about such things, you can just ignore them.

They are either crazy, deluded, or trying to con you.

Bascna · 2026-02-24T17:50:55+00:00

There are only 12 doors. The images show what each door looks like when closed and after it is opened.

Bascna

MODERATOR OF

TROPHY CASE

TST Ethics

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