Mr. Friend

My son's favorite stuffed animal growing up was a frog he called Mr. Friend.  It was hard not to like Mr. Friend.

Jet Jaguar Can Deadlift

 

Cow Power!

There was a small older fellow who lifted competitively at the UT Longhorn Open years ago, and he inspired us all with these kinds of sayings...

AI Caught Making an Error - Oops!

When I ask AI questions usually, either it doesn't make any error, or it makes errors I don't notice.  But this time it definitely made a noticeable error.  I asked it to verify the number 1984 in binary, and I believe 11111000000 is correct, but that translates only to 1024+512+256+128+64.  There should be NO 32 in the sum as AI stated here.  

The 11111000000 stands for 1*2^10 + 1*2^9 + 1*2^8 + 1*2^7 + 1*2^6 + 0*2^5 + 0*2^4 + 0*2^3 + 0*2^2 + 0*2^1 + 0*2^0

Hope I typed all that out right and didn't make an error myself.

Have it Now is the New Way to See

Years ago I wrote a satirical variant of Billy Joel's "It's Still Rock and Roll to Me."  Not an improvement, and probably hasn't aged well.  But I don't think I published it anywhere, so might as well put it up now:

“What’s the matter with the song I’m playing

Will you tell me that it’s not the time?

Maybe I should sing of fame and fortune

And pretend that everything is fine

Nowadays everybody wants something sunny

Guarantees of fancy cars, and piles and piles of money

Everybody’s pushing all this new style on me

‘Have it now’ is the new way to see

 

What’s the matter with the way they’re thinking?

It just seems like a twist of time

Back in old days things weren’t as easy

But there wasn’t nearly so much whine

Nowadays people go dancing all around town

They have tons of fun while their love of working goes down

Good days, good pay, good times, all the way

‘Have it now’ is the new way to see

  

Oh, we get up every morning and we see in the paper

More bad news that we’ve already seen

Scientists working oh so hard everyday

To find the reason for every bad thing

Try to keep it all running

 

How about signing up with big business,

Where you use all of your great wit?

We can say for sure that you’ll love it

And you’ll never want to call it quits

You know if you say ‘no’ that you’ll get weaker

But saying ‘yes’ will make you a great and rich speaker

Oh man, what a plan, get it now, while you can

‘Have it now’ is the new way to see

 

Best of all it’s not considered cheating

And there can never, ever be too much

Once you get your foot in the door and make money

 You’ll never, ever lose your touch

Good days, good pay, good times, all the way

‘Have it now’ is the new way to see

 

Everybody’s pushing all this new style on me

‘Have it now’ is the new way to see”

 

My Best Man

One of my favorite people ever was the guy who was good enough to be best man at my wedding.  He was a handsome, fun, and talented fellow.  Studying mechanical engineering and could bench press over 400 pounds.  This boosted his ego to the point that some people found him somewhat insufferable despite the high amount of charisma that he also possessed.  But I loved it because he reminded me of all of the heels I watched on professional wrestling.  So I did my best to actually feed his ego even MORE just to see what happened.  It was a lot of fun, and he seemed to eat it up.  It sure was an easy way to become his friend.

But at the end of the day, he was smart and sensible enough to realize his limitations (even though he'd never admit them out loud) and never let his ego get TOO out of check as to be unhealthy in a way he couldn't handle.  His life never became unstable, and he ended up working at Lockheed Martin for many years.  I hope he's still doing well.  Because even though it seems like I just fed his ego as some kind of joke, I really did like the guy.  He was my best man for a reason.

The Desire For a Vision

Some people really seem to want to have a spiritual vision at some point in their lives.  Either to confirm their faith, or just because it sounds like it would be something really interesting to experience.  But I'd rather not experience such a vision myself.  In Biblical literature, God never has a vision for somebody unless he also has a special mission for that person.  Usually a difficult one.  That alone kind of puts a damper on my desire for any kind of spiritual vision.  I think I'm fine without one.  Especially since I quite enjoy that blurry line between fantasy and reality.  I wouldn't be a pro-wrestling fan if I didn't, or a fan of imaginary numbers and the interesting properties of holomorphic functions.

Perhaps an unconfirmed faith is sometimes best.  It's not like we'll be able to confirm everything we wish for in our lifetime anyway.  I'm in my mid-forties and I know for sure there are a lot of things I will never know before I pass away.

Maybe I had mysterious but meaningless visions before without ever knowing they were visions.  I believe I briefly mentioned in a prior post before something about an older woman in one of my community college art classes back in 2001, and her husband was a holocaust survivor that challenged me at arm wrestling one time.  As far as I know this was reality.  But can I verify it or can anyone else verify it either?  Probably not.  So someone can claim it was a vision and how can I prove them wrong?

Graphing Congruences in Modular Arithmetic And Turning a Cartesian Graph Into a Polar One

Even though this isn't anywhere close to Fields Medal level stuff, and it's not very deep, I think it's still pretty cool.  I haven't seen it before, but I'm pretty sure someone somewhere already did something like this.

What if we want to transform a graph in cartesian coordinates into one that looks like polar coordinates, where the x-values circle around some center point, and the y-values measure a distance from that center?  X would be comparable to Theta and Y would be comparable to R.  So we'd do a transformation as follows:

Theta = X times (( 2 times pi ) over a modulus)

R = Y

This modulus would cut the distance we have to travel around the center point into equal pieces.  We'll use the modulus 7 for this demonstration.

So if I wanted to take the arbitrary function Y=X^7 (this is an unrelated 7 - sorry I'm using the same number twice) and graph it in this system, I could do so, but first I'd have to do some easy algebra and express X in terms of Theta instead of Theta in terms of X.  Just divide both sides by (( 2 times pi ) over the modulus 7).

We end up getting R = ((7 times Theta) over (2 times pi)) raised to the power of 7.  That is something we can graph in Desmos.

Now, if I cut the distance around the origin into 7 parts, it would just be the angle Theta = (( 2 times pi ) over 7).  For some reason Demos really doesn't like me graphing that and won't let me do it, so I use the graph Y = tan(( 2 times pi ) over 7) times x, since that's the same thing.

So this line shows one-seventh of the distance around the origin.  But only the upper right part of the line stemming from the origin.  The lower left part is just a continuation of it, and does not represent another portion of 7 parts around the line as far as I know.

Modular arithmetic would tell us that once our Y=X^7 equation crosses this line, that equation is congruent to 1 (mod 7) at the R value where it crosses.  When the equation crosses the right side of the x-axis, that's when it's congruent to 0 (mod 7).  We could do this with other values as well if we were willing to draw more lines (and I'm not).

Anyway, we can test it out.  Here in this picture, we see that our X to the 7 function, the red curve, crosses the 1 (mod 7) line, the green line, right where that blue circle is.  The blue circle is just R = 8^7.  A pretty big number.  Over 2 million.  Is it congruent to 1 (mod 7)?  Indeed it is.  It's equal to 299,593 times 7 plus 1.  

Let's try another one.  This time we see the graph crosses the line at another purple circle, much larger than the last blue circle.  In fact, the blue circle at R = 8^7 looks almost like a small dot here.  This purple circle is R = 15^7.  Is this also congruent to 1 (mod 7)?  Sure is.  It's equal to 24,408,482 times 7 plus 1.  Nice to see computers confirming what the math shows.  And it's fun to graph this thing and zoom in and out on it.  Reminds me of the old Spirograph toy from a long time ago.

And that's all I've got to say about modular arithmetic here.

Now I want to do a conversion of a cartesian graph into a polar one using this same transformation, just because I think it looks interesting.

Let's do a nice and easy graph of a system of linear equations and note their intersection point.  Here the diagonal green and blue lines intersect at the red x=1 line and the orange y=7 line.

Applying our transformation to this system, we see the red x=1 line is now diagonal at the origin, the orange y=7 line is now a circle, and the two diagonal lines that cross each other there have become some kind of crazy spirals.  Very complicated looking.

So I just took something nice and easy and made it way more complicated for no reason.  I just think it's something kind of worth looking at, at least for me.

Proverbs 21:30

Proverbs 21:30 states "There is no wisdom, no insight, no plan that can succeed against the Lord." 

This verse is really about the futility of going against divine authority, but for some reason it reminds me of a common implication that if there is no final authority, then anything is permitted.  This is a common argument in apologetics I believe.

And vacuous truths, which I mentioned not too long ago, look somewhat similar.  If the premise is false, then any conclusion is permitted.

So if there isn't a God, apologists would say anything goes using their usual arguments.

But also if there is one, and we declare there to not be, again we'd reach the conclusion that anything goes, using a vacuous truth argument.  (Or if Proverbs 21:30 turned out to be true but we believed we had insight that was against the Lord.  Then any conclusion would go there too.)  

So in declaring God as a falsehood, whether accurate in actuality or not, apologists are going to reach the idea that anything goes.  Either using a standard argument or a vacuous truth one.

Certainly not a brilliant observation or anything, but a questionable and minor observation easy to put in a personal journal for a day. 

The Black Sun

I was fortunate enough to witness the April 8, 2024 solar eclipse in person.  I had to travel a bit to reach the path of totality, but it wasn't terribly far.

The experience was a bit different than I pictured it would be.  Instead of it feeling like nighttime in the middle of the day, it was more like a sunset in the middle of the day, where it didn't get near as dark as night, but still much darker than it usually is during the day.  It was enough to hear the sound of roosters crowing in the distance.  

But it was odd to look up at the sun and see it completely black in color.  I took a picture with my phone, but I guess since I didn't have any special photography equipment, it didn't capture the moment correctly at all, and the sun looks pretty much as bright as normal in the picture.  

Still, as short as the experience was, and as disappointing as my documentation of it was, the memory of the sun completely black in the sky with a glowing ring around it sticks with me.  Definitely a once in a lifetime experience.  I'll never see it again.

Why There's No Quintic Formula - The Easiest Explanation I Have So Far...

Here's currently the best explanation I have of why there is no general formula in radicals for the roots of a quintic polynomial. It's more for my quick reference than anything else. It may not be totally accurate but maybe it's close.

Vieta's formulas put the roots of a general polynomial equation with unspecified variable coefficients in a position to be swappable, but potentially roots nested inside other roots can pop up, and they can't be easily swapped if they're not conjugates. If a general quintic formula in radicals existed, it would violate this conjugate swapping structure.

I think the biggest pitfall I've gotten caught in is not realizing that the only requirement for SPECIFIC examples where we already know the coefficients is that they respect the nested conjugate rule and don't violate it. Their roots don't have to be all swappable with each other. But when we don't KNOW the coefficients and are dealing with a general variable-coefficient case, we have to allow all roots to be swappable because a specific polynomial may potentially have that property.

These ideas build on a video I uploaded a while back here: https://www.youtube.com/watch?v=qOHkF26EKfg

A HUGE Difference Between Worldly Thought and The Teachings of Jesus

It seems common in our culture today to get as close as you can to the line without crossing it.  Get as drunk as possible at parties, as long as you don't become an alcoholic.  Date as young of a lady as possible as long as she's over 18.  Cuss and get in someone's face as much as possible, as long as you don't pull out a gun.  Stuff like that.  

This is very much the opposite of the teachings of Jesus.  His teaching advocates taking extreme precautions against even the potential to sin.  That's probably why he implied that it was worth sacrificing even a limb like an eye or a hand if it meant keeping you far away from the kingdom where permanent sin dwells.

Even from a secular standpoint, Jesus's teachings make a lot of sense.  Just for precautionary reasons if nothing else.  Why put yourself unnecessarily in a situation where you have so little room for error?  Can someone call themselves anything other than foolish if they accidentally step over a line they spent so much time treading?  

Weak Argument Against Vacuous Truths

Vacuous truths never felt intuitive to me, ever since I first learned about them.

Here's one reason why.  It's a weak reason and not a strong reason.  But it's strong enough in my potentially deranged mind for me to feel I should mention.  Forgive me if there are any typos, because they are pretty easy to make here.

Look at the statement NOT(if A then B) and the statement A and NOT B.  They both have the EXACT same truth table, if you draw the truth table out or ask a competent AI program to do it for you.

But I would argue A and NOT B is actually a stronger statement than NOT(if A then B), making the statements not equivalent.  A and NOT B is clearly not a conditional statement.  A happens no matter what.  Does A also happen no matter what in the statement NOT(if A then B)?

Suppose A doesn't happen and B does.  Is this an instance of NOT(if A then B)?  What if A doesn't happen and B also doesn't happen?  Also an instance of NOT(if A then B) perhaps?  I would say anything whatsoever that is anything other than if A then B fits the criteria of NOT(if A then B).  

Let's try an example to flesh out this line of thought.

Think of the actions of A and B being the following:

A = the action that you honked your car horn yesterday

B = the action that your car windshield broke.

There are four possibilities involving your horn and windshield yesterday:

1) your horn honked and your windshield broke

2) your horn honked and it didn't break

3) your horn did not honk and your windshield broke

4) your horn did not honk and your windshield didn't break.

Which of these 4 possibilities fit the 2 statements NOT(if A then B) and A and NOT B?  

A and NOT B would say that you definitely honked your horn yesterday and your windshield did not break.  Only possibility #2 fits that.

NOT(if A then B) would say it's not true that if you honked your horn yesterday, then your windshield broke.

If you did honk your horn, then only possibility #2 would fit that.  If you didn't honk your horn, then we don't know what would have happened for sure.  But mostly likely honking your horn wouldn't actively have caused your windshield to break.  This is NOT A and NOT B. Possibility #4.

Is possibility #4 a subset of the statement "it's not true that if you honked your horn yesterday, then your windshield broke"?  I would say yes, based on probabilistic assumptions alone. The only way this would have been true is if some mischievous individual installed some device in your car on purpose that would smash your windshield every time you honked your horn.  At least if you interpret the conditional if/then as definite cause and effect and not just random occurrence of each.  

We could alter our truth table for this specific example, but if we wanted to make a general table, we'd probably have to set up a U for unknown on vacuous truths.  Or maybe M for meaningless.

Still, there are pros and cons to using U for vacuous truths. They're more conservative, but they leave the logical system open instead of closed.  Plus they introduce a ternary or three-valued logic system (which some logicians already have invented) and they're a bit more complicated than logics with truth values only limited to T or F.

So even though I don't think vacuous truths always adhere to reality despite being pushed as such, they do allow closure in a fairly simple logical system, and there are definite benefits to that.  Not worth changing, but probably worth questioning more than they're currently questioned in introductory logic classes.

The American Dream

One of the most popular wrestlers ever was Dusty Rhodes, who symbolized the American Dream.  The American Dream was his nickname as well.  

Most people equate the American Dream with owning a home, but it can pretty much be anything.  My dad was quite impoverished growing up, and when his mom said she didn't have any money to buy him a Coca-Cola Classic, he said when he grew up he was going to get a refrigerator stocked with plenty of Coca-Colas so he could have one whenever he wanted.  With this determined mindset, he went to college in Louisiana where he struggled to pass calculus, taking it three or four times before he finally got the credit he needed, and ultimately became a civil engineer.  Today he has a refrigerator and I've never seen that refrigerator without a Coca-Cola inside.  The man lived his dream.

When my wife was growing up she always wanted a super-fluffy cat.  But this proved a greater challenge than she thought initially.  She wasn't able to get one right away, and then had a sweet cat she dearly loved that lived to be at least 20 years old.  This cat wasn't fluffy, but he was her best friend and kept her very happy.  When he passed away, it broke her heart.  Then she finally decided it was time.  She ended up getting the super-fluffy cat she always dreamed of, even though it took a few decades.  She still misses the cat that was her best friend, but she loves her super-fluffy cat too.  

And when I was in high school, I loved wrestling even more than I do now.  I watched old stuff from the video store, and watched either WCW or WWF every week for a good four years or so.  Always looked forward to the Monday night Nitro or RAW that followed the monthly Sunday pay per view in particular to find out what happened at the big show.  I did purchase a few pay per views, but they were at least $60 a show, so I probably bought fewer than I could count on one hand.  I bought a few VHS tapes as well, but they were $30 each, and that's a lot of money to a kid with no job.  Couldn't buy very many of them.

I said one day I'd watch all those pay per views I couldn't watch growing up.  Then I found out about the WWE network, I guess not too long after it came out.  Every pay per view I ever wanted to watch was on that network, for a reasonable monthly fee.  But even though I had a degree and a job at that time, I was married and still didn't have quite enough money to buy the subscription.  Or the time to watch it for that matter.  I said when I finish grad school I'll get the WWE network.

Well, eventually the network was acquired by Peacock.  So I said I'd get Peacock when I finished grad school, and I didn't have but a few classes left at that point.  But then my wife tells me she's getting Xfinity for our TV service, just because it came with our internet.  And Peacock was included for free.  So just a few months before finishing grad school, I finally got to watch all the pay per views I wanted to watch.  In particular I wanted to see the Shawn Michaels and Undertaker cell match from Bad Blood 1997.  And I finally got to see it after 23 years of waiting.  I got to live my dream.

Now a lot of those matches are on the WWE Vault and WCW YouTube channels for free, and Netflix has the WWE pay per view library also.  But the main thing is I got to live my dream.  Just like my dad got to live his, and my wife got to live hers.  Even though it took each of us a while to get what we had our hearts set on.  We lived the American Dream.

Hulk Hogan Sign from WrestleManias 6 and 18

This is kind of amazing to me.  In April of 1990, WrestleMania 6 took place in the Skydome in Toronto, Canada with Hulk Hogan vs the Ultimate Warrior in the main event.  And you could see a big banner of Hogan clearly in the audience as the Ultimate Warrior made his entrance.  

https://www.youtube.com/watch?v=IRtOTIykZNE

A full 12 years later, WrestleMania took place in the Skydome again, with Hulk Hogan going against the Rock in a highly anticipated match at WrestleMania 18.  And either the same exact banner or a REMARKABLY similar one could be seen in the audience as the Rock and Hogan stared each other down.  The only difference is it's in a different seat this time.  But pretty much the same sign, in the same building, with the same wrestler in the match.  Twelve years later.

https://www.youtube.com/watch?v=eJ9zibElS5w

Sparing the Rod and Spoiling the Child

This old phrase is often attributed to the book of Proverbs.  It has fallen out of fashion in recent years due to the increasingly negative view of corporal punishment in the western world.  But if you generalize it beyond the meaning of corporal punishment, there's something interesting to note.

It really implies that the wise party should never yield control to the unwise.  And not even because of the adverse effects on the wise, but because such yielding does NO favors for the unwise either.  Power in the hands of the foolish does not aid the foolish in any way that matters.