The Insane Math Behind Near-Integers

I think one time I got curious about that crazy looking infinite series that Ramanujan sent Hardy out of the blue to initiate their collaboration, and other than it being so complicated in appearance, I wondered what as so special about it.  So I began using AI to investigate because I'm lazy and also because I didn't feel like driving up to the UHCL library and paying the parking fees.  I found out the series converges very quickly, and this is the driving idea behind near integers.  If a series converges to an integer quickly, the first term should be pretty close to an integer.

There are probably a few ways to get fast convergence to an integer, but what this kind of math uses is something called the j-invariant.  Every complex plane lattice has a j-invariant number, and this invariant is unique to the lattice shape.  So if you scale or rotate the lattice it doesn't change the j-invariant.  This j-invariant number can be represented as an infinite series, which I am not sure at this moment how it's computed or derived.  I believe the work of Jacobi was used to relate all of the values of the lattice into a unit disk somehow, and that's how the series appears and converges quickly.  And there are special instances where this j-invariant is guaranteed to converge to an integer.  

Now the j-invariant involves a tau value determined by the lattice's periodic values, and that tau value determines the lattice shape.  And when you can get this lattice to map to itself, it's a very special scenario.  It's called complex multiplication.  And I get really fuzzy here because a lot of stuff seems to happen at once and I have no idea what order to describe it in.  As if I weren't already fuzzy on the subject to begin with.  I could be getting a lot of stuff wrong.  But, as I understand it, now we're dealing with lattices in the complex plane, and unlike real numbers complex numbers may or may NOT have unique factorization.  But a clever way was invented so there could be a kind of unique factorization with these things, and that's why something called ideals were invented.  Ideals always factor uniquely, even with complex numbers.  

But from what the imperfect but seemingly well-meaning AI interfaces tell me, each lattice IS an ideal.  And the lattice represented by a tau value for a j-invariant is going to factor since it's an ideal.  The values of the lattice factor into multiple factorizations, and each of those factorizations can form its own lattice.  

Now here's where the complex multiplication self-mappings get really interesting and get to the heart of the whole set-up of tying unique factorizations to exact integer values, which makes the whole near-integer stuff work.  When an ideal maps to itself, it means the mapping operator can at most permute the factors among themselves.  And this puts it into Galois permutation territory.  With this Galois permutation stuff, the sums and products of the factors are going to be whole numbers.  Not sure why this is, like I should be, but I believe that's the case.  So if you only have only one factor as in unique factorization, the sum and product of all factors is going to be whole, which means your j-invariant is going to be a whole number.

So that's what relates unique factorization to exact integers, and what helps us get an integer j-invariant with a near-integer first term in the fast-converging series.  

I was hoping to do a better rough sketch of an explanation, because I'm not exactly super happy with this one, but I think it's probably the best I can do for now.  Hopefully I can do some edits here and there later, and get a better idea of what ideals are.

Moral Nihilism is a Garbage Philosophy

In the past I have attacked moral relativism as contradictory, but I could not accuse moral nihilism of that.  Still can't.  But that doesn't mean I can't call moral nihilism a garbage philosophy, even if it's logically consistent.  I also feel comfortable claiming it's a philosophy from the devil himself.  If these sound like ad hominem attacks, that's because they actually are ad hominem attacks.  But moral nihilism is so weak, it can't even argue that ad hominem attacks possess any less moral worth than actual solid arguments.  That's pathetic.

A fulfilling life requires two things.  It requires a meaningful path to pursue, and it requires the courage to actually take that meaningful path.  Moral nihilism removes both of these things, calling them not worth the effort, and equating them to stagnation.  It removes the inalienable rights of life, liberty, and the pursuit of happiness from the declaration of independence and equates them to death, enslavement, and the helplessness of perpetual misery.  

What's sad is this philosophy attempts to mask itself into something honest, implying that since we can't know moral absolutes, it's best to pretend they don't exist.  As if this philosophy knows what the best of anything is.  Best isn't in its vocabulary, at least not in the rare event that its adherents are being consistent with what they claim to believe.  In this philosophy a lie is not in any way inferior to the truth, but how often do we hear moral nihilists say that?

Abandon moral nihilism and treat it as worthless.  After all, it declares itself to be so.  

Man Created the Integers - All Else is the Work of God

A mathematician named Kronecker once said, "God created the integers, all else is the work of man."  And it's hard for me to imagine how he said that.  He was obviously more advanced at mathematics than I will ever be.  But the properties and results that flow from just a few mathematical rules are just so mind-blowingly unexpected I don't see how one could have argued that they were intentionally created instead of discovered.  

It's very easy to create the concept of an integer, but no one in the world would have thought of the argument principle in complex analysis.  No one would have intentionally created the Basel problem to sum up to its result either.  These were unexpected discoveries that seemed to stem from nature itself.  

Kronecker was apparently something called a constructivist, and I believe most of mathematics has not taken this approach.

Was I Closer to God When I Sinned More?

When I was a young man in my early 20's, I couldn't shake the sin of adult websites, even after several years.  And as awful as that is, despite the rest of the world thinking it's fine, that enslavement did keep me in quite a bit of prayer.  At times I felt like the tax collector in the parable mentioned in Luke 18.  And now sometimes I wonder if I'm more like the pharisee in the parable, which of course isn't a good thing.  I still fall prone to anger and sloth and many other sins, sometimes perhaps worse than the sin I used to do, but I don't pray quite as much for forgiveness now, or even pray as often for any other reason.  I think I primarily pray now for guidance during life's upcoming challenges.

But even if I was closer to God then than I am now, I can't WILLINGLY go back to the sin that God delivered me from 16 or so years ago.  Biblically it would be like a dog returning to its vomit.  That's a path I can't knowingly justify.  It may still happen, but if it does I won't be happy about it and I believe I will be quite devastated.

It kind of reminds me though of my favorite episode of Star Trek The Next Generation, the one titled Tapestry.  Where Picard learns that the unflattering parts of your past are so engrained in your life story that you can't really unravel them, and even if you could it would lead to unexpected and potentially undesirable consequences.  I might have mentioned that episode in this blog before because I love it so much, even though I am not sure if the message is 100% true.

But if I ever need to be reminded of my continued sin, all I need to do is read about turning the other cheek regarding personal affronts.  That's a HARD verse to obey and I definitely know I'm guilty of not obeying it.

Your Effort is More Important than Who You Vote For

Something that puzzles me is the emphasis on who you vote for.  Sure, it's an important decision and should be given due diligence if possible, but is it really more important than the labor your put into your job and your family day in and day out?  You really think pulling a lever once every two years or so can substitute for a requirement like that?  Maybe if your labor is light, or meaningless, then you might have that opinion, but I can't imagine any consistent amount of labor possessing that quality for that long of a span.

Vote for whoever you feel called to vote for, but realize that voting is just one part of your life, and MANY other votes are considered besides yours.  Your vote is your decision, and people have fought and died for you to have the right to decide it.  But don't ever think it can substitute for the other efforts you need to put into your life to be a good and worthwhile citizen.

Believing Magic is Fake Doesn't Add Much IQ

Will your SAT score automatically go up more if you give up your belief in a holy book with magic in it? The answer is no. However, it WILL go up more if you study and practice problems, regardless of your beliefs regarding magic.

You will not master intellectual content unless you expose yourself to it. You can't expect to learn probability or the binomial coefficient just by saying you don't believe in magic. Skepticism is not a substitute for opening a STEM book and absorbing the content within.

Anyone that believes that adopting a "magic is stupid" philosophy is sufficient to rank them among the highest of the high in terms of intellect is being severely misled. Going to take A LOT more than that.

Math and Science Made Me Believe in Miracles More

Events can only be scientifically confirmed when they're a part of a controlled, consistent environment.  Is real life outside of a laboratory ALWAYS controlled and consistent, without exception, as the philosophy of determinism insists?  Impossible to prove, but I would say the odds are not good.  Reality has no obligation to fit inside of the small box of required criteria to always make sense to our nature-created brains.

After studying a bit of the natural sciences over the years, particularly mathematics, I've come to discover that rare, uncontrolled events simply have no part in a scientific experiment.  It's not that they can't possibly exist so much as they can't possibly be detected through the scientific method.  These kinds of events cannot be verified scientifically ever, whether they have the ability to exist or not.

In the admittedly stupid movie titled, "A Talking Cat!?!" the feline protagonist Duffy attempts to help a few mentally lost people with some of their life problems.  He talks to each of them separately, but explains he can only talk to them once, never really giving us a satisfactory explanation of why this is.  Now if a situation like this ACTUALLY happened outside of an imaginary story, the only evidence we'd ever have of it is eyewitness testimony that's not worth believing.  No one can control when Duffy chooses to talk.  For all we know he never spoke to anybody else other than these few dimwits.

So it does help to know the potential limitations of the scientific method as well as its incredible strengths.  It's clearly the best tool we have for understanding the physical aspects of reality, but that alone isn't enough to make it infallible.  Weird and rare events that happen to only a few unreliable people can still potentially pop up without the scientific method ever acknowledging their reality.  Only a deterministic philosophy, which encompasses FAR too much to be proven by empirical methods, places a limit on such possibilities.  

But even if eyewitnesses claim such events occurred, I think I'll be like Arthur C. Clarke and remain skeptical of such claims.

Condemn, Tolerate, or Embrace?

I think I remember my son getting some sort of Minecraft strategy guide a long time ago, and it classified sentient objects you encounter as either benign, neutral, or aggressive.  And that reminds me of the response people can have towards behaviors.  They can embrace the behaviors, tolerate them, or condemn them.  

Notice the distinction between tolerate and embrace here.  They are not the same thing.  Tolerance is comparable to allowance in the form of ignoring a behavior without any active participation.  Embracing on the other hand consists of genuine involvement and enthusiastic approval with repeated encouragement.  Tolerating and embracing are two very different responses to a behavior.

Moral and Mathematical Constraints

The citytutoringmath YouTube channel, while perhaps not correct on everything, certainly does an excellent job repeatedly reminding us that true liberty is not the absence of constraint, and that a lack of self control leads to chaos rather than liberty.  When we rid ourselves of all forms of discipline, we do not get a utopia and instead get quite the opposite.  Sin must never be given a playground in which to run around unencumbered.  Even though this should be obvious, it's frankly shocking how often we get an impression that so many people believe the opposite regarding self control.

But what I thought about recently is that while moral constraints are necessary for society to achieve and maintain prosperity, mathematical constraints can be just plain interesting and add spice to someone's mathematical life.  Fermat's Last Theorem is trivial if you allow all reals and don't restrict the solutions to integers. But when it gets restricted it becomes MUCH more interesting.  So interesting I can't even follow it.  When Diophantine Equations start going into imaginary number rings, that non-decimal constraint they throw up can cause things to get wild in a hurry.  I believe I mentioned this in a previous post about 26 being a special number in that it's the ONLY number exactly one after a perfect square and one before a perfect cube.  You start going into imaginary numbers to solve a problem involving integers.  Crazy, but true.

The Most Abused Bible Verse Today? - Matthew 7:1

"Do not judge, or you too will be judged."  A verse that is used extremely often to justify any action (even unbiblical ones) on the grounds that it should be left up to - not the final judge - but no judge at all.  Clearly this is not the intent of the verse.  Let's think about what the intent may be.

Obviously only God can judge a man's final destination.  Because even if a man is as lost as can be, God can save him at any point.  So mankind clearly lacks both the ability and authority to condemn the soul of one of their own.  And I do think this verse warns against attempting to judge a man in such a manner.

I also think the verse warns against judging too harshly.  A man should treat others fairly in order that he can attempt to justify that he himself should be treated fairly.  But this is where the verse starts to get abused.  Fair gets twisted into soft.  And as the evaluation softens, the standards soften too.  We start judging even the hardest crimes with the softest consequence.  I do not believe the verse ever intended such a result.  

Low standards are not a good way to live.  Particularly since the standards of Jesus were quite high.  Loving your neighbor is a very high standard.  But if you twist this verse enough, you can get the depraved thought that harming your neighbor should not be judged harshly at all, in case we decide to cause some harm to our neighbors as well and are now accountable to a harsh result.  Why should we not reap a harsh result for harsh behavior?  I cannot find a Bible verse anywhere that states a person who commits a harsh crime does not deserve a harsh consequence.  Just because God grants a sinner grace does not mean the sinner is entitled to it.  

Matthew 7:1 was never intended in any way to be carte blanche to do as you please without fearing any kind of condemnation from your fellow man or from the scriptures.  A primary purpose of the scriptures is to judge and condemn sin, so that conviction will lead to confession and ultimately repentance.  In citing the Lord's Prayer, as Jesus taught us to pray, we ask for our sins to be forgiven.  We do NOT ask that the sins we engage in never get judged as sinful.

So I believe we are to avoid the judgment of souls entirely, to judge current character only when prudent and then only very carefully, and to judge actions according to how Biblical doctrine specifies those actions.  If scripture calls it sin, we need to call it sin as well.

Pros and Cons Between Generations

I hear generations fight with each other about which had it easier.  And I think back and realize how I struggled finding a job after getting a college degree, and my dad didn't struggle with that quite as much. And I probably won't have as good of a retirement as he had either.  But ALSO he had a MUCH rougher childhood.  He didn't spend most of his time playing video games like I did.  Nor did he have anywhere near the level of toys I had.  He worked at his dad's gas station without pay.  And even when he had free time the entertainment he partook in wasn't near as sophisticated because video games weren't even invented back then.  My childhood was MUCH better than his even if his adulthood might have been a bit smoother economically than mine.  Also he studied engineering and I studied math, so that might have made a difference as well.

But of course, that's only the economic prosperity part of the equation.  Some people who have less still enjoy what they have more than those with a greater number of possessions.  And as much as I enjoyed my childhood, I actually enjoy my adulthood more.  It's not as economically prosperous, but life is about much more than how many toys you have to play with.  Sometimes it's about your mission, even if that mission is mostly unglamorous minor responsibilities that won't change the world or anything.  They're important to me and a few other people, and I think they're important to God as well.  God cares about small things, even if it doesn't always seem like he does.

Wasted Potential is Worse than Wasted Effort

Ecclesiastes chapter 11 says that whoever watches the wind will not plant.  

A man like this finds weather conditions for planting to be unideal every time he contemplates the endeavor.  So he never does it.  This is an example of a man saving effort by wasting potential.  

Compare this to the main that waits for tolerable conditions to plant instead of ideal conditions.  Or even one that plants in conditions that may be extremely far from unideal because he has no choice.  He may be wasting his effort, because the seeds may not grow.  But if they don't, he's ultimately not much worse off than the man that didn't plant at all, and may actually be substantially better off if luck is on his side.

The man that never planted at all only has one thing as the result of his effort-saving.  An excuse.  "Well, the weather wasn't good," he might say.  And he might be correct.  But that will be of little comfort if his neighbor DID plant in weather that wasn't good and actually got something as a result of it.  Are excuses really so comforting that they're worth wasting potential on?

I see this in young men online who get discouraged by the admittedly bad job market.  Entering the job market wasn't easy for me in my 20's either, and I remember the job search not being a fun experience.  I don't want to go through it again if I can avoid it.  I can sympathize.  But it never entered my mind at that time to totally give up on working for a living, because I knew that wouldn't end up going well.  I wanted to at least TRY to ultimately end up with more than just an excuse in my life if I could.  I'd rather fail making the continuous attempt and wasting the effort than not even make the attempt and waste the potential.  And in my case I did fail for a while, but not forever.  What at that time seemed like an eternity of wasteful effort is now in the long-distant past.  The effort ultimately paid off, and I believe more often than not, effort tends to do just that, if someone can just hold out and exercise consistency and patience.

So anyone in a tough position where effort doesn't feel like it's going anywhere, remember the trade off, and keep taking the chance.  Because wasted potential is even worse.

My Mom's Garfield Collection

My mom passed away many years ago, but she used to buy stuffed Garfields all the time as a hobby, and put little outfits on them that she got from other stuffed animals at places like Goodwill.  Later on my dad made some awesome display cases for them in reverence to all of her work.  I am unsure what I will do with them after my dad passes, but it would be nice to have the collection on display somewhere.  I don't want to just throw it out, but I have no room for it myself.

 

Anti-Villain Example In the Anti-Hero Age

One of my favorite YouTube channels now is citytutoringmath.  I like it because it's an interesting combination of mathematics and Biblical doctrine - two things I've always enjoyed and don't often see put together in one place.

Now many years ago, intellectual pursuit and Christian devotion were seen as positive things.  This was before the current age of the anti-hero who rejects tradition and many honorable things that go along with it.  I guess it makes sense that when destructive activity is heralded that constructive activity would be shunned.  That's how it was in the movie Danger Diabolik.  But the guy behind citytutoringmath does seem to fit a villainous persona as well, in that he speaks fairly aggressively and could care less about the feelings of his listeners and how sensitive they are to the less-pleasant aspects of his message.

So citytutoringmath gets my vote for one of the best anti-villains in the world today, and I kind of want to see more of his kind.

Problems With The Term "Woke" And A Potentially False Mathematical Implication

Possibly the biggest problem I have with the woke movement is the choice of the term it uses to represent itself.  It's not called "social justice woke" or "sexual orientation woke."  It's simply called "woke."  While this might simply be born out of convenience because one word is a much quicker and easier abbreviation for a concept than three words, I still think this possibly inadvertent simplification seems to imply a level of awareness that stretches far beyond its reach.  

While social injustice awareness is certainly not a bad thing, I believe it becomes a bad thing when you imply that's the ONLY skill anyone is required to possess in this world in order to be classified as fully aware and enlightened to the point that no other knowledge or skills are required.  Even if you can't count or read, and you've never expended any effort beyond sitting around and doing drugs all day, you're still fully aware of everything that matters simply because you recognize bigotry exists?  I would disagree, because I would argue that bigotry recognition is a NECESSARY but INSUFFICENT condition for cultural awareness and enlightenment.

The words necessary and sufficient form an important pair of terms in mathematics.  When a two related conditions in a statement fit both of these criteria, the statement carries a special kind of relationship between conditions known as a biconditional.  Biconditionality implies equivalence.  True in both directions.  Necessary implies truth in one direction and sufficient implies truth in the other direction.  What I claim regarding bigotry awareness and true enlightenment is that the two conditions are NOT connected by a biconditional.  Instead I claim these two things:

1) If one is fully enlightened, then indeed one automatically possesses an awareness of social justice problems

2) However, if one possesses an awareness of social justice problems, that person is still NOT automatically fully enlightened, because true enlightenment and awareness has other unrelated requirements as well

Notice with these two conditions, the flow is automatic in one direction but not the other.  It is a conditional statement but not a biconditional statement.  For two conditions to be equal, the biconditional must be satisfied, so that if either one of the conditions is satisfied, the other will automatically be satisfied as well.  That's not happening here.  So the two conditions are not equal.  Being truly enlightened is not equal to being aware of social justice issues.  Why?  Because being truly enlightened requires more than just that alone.  When one condition or set is strictly bigger than another, like true enlightenment encompassing more than just social justice awareness, they can't be completely equal.  Even if social justice awareness is the BIGGEST part of being truly enlightened, it's still not fitting all the requirements for full enlightenment and awareness.  

Now it might seem petty on my part to make a claim that the woke term implies far more than it does, and honestly it might be some kind of a stretch.  I believe the formal phrase for that type of petty stretch action now is called "seeking a microaggression."  Is that something that's permitted in two political directions or only one?

Misconceptions About Relativity

There's a big misconception about the theory of relativity in physics.  It does NOT imply that absolutes don't exist.  It just implies that space isn't an absolute and time isn't an absolute.  Also, very importantly, it implies that the speed of light measured by an inertial observer in a vacuum IS an absolute.  There are other absolutes also, but I don't know them all that well and don't feel like going into them here.  Ask AI if you want to know them.  The point is NOT EVERYTHING IS RELATIVE even in this theory.  There's at least one thing that isn't.

But some people don't want to look into things that deeply.  Instead they hastily develop a class of thought based on the faulty premise that because certain things we previously believed to be absolute turned out otherwise, then nothing is absolute.  This is false.

Whether morality has no absolutes is technically still up for debate I guess, but moral relativists can't really use the scientific theory of relativity to back their claim, because that theory DOES claim absolutes, even if it sounds like it doesn't.

Quote From A Tree Grows In Brooklyn

"It would be considered beautiful except that there are too many of it."

I believe this quote is in an isolated spot on one of the pages before the actual start of the novel, if I recall correctly.  I love this quote because it sums up reality pretty well.  There are so many amazing things out there that our brains can't process it all or even detect it all.  A lot of beautiful stuff gets no attention as a result.  Kind of a shame, but there's not really anything we can do about it.

The Elephant in the Room - At Least With Modern-Day Christianity

Fornication.  Very prevalent.  Hardly ever mentioned.  How much is homosexuality mentioned in the Bible?  Maybe about five times?  Adultery and fornication are mentioned more.  Much, much more.  Probably a reason for that disparity in emphasis somewhere.  

Let's face it.  Fornication prior to marriage, or even as a substitute for marriage, is something most of us in this day and age have been guilty of at some point - even myself for a short time.  It has become extremely tolerated in the western world, and as a result I believe the church has softened its approach with it.  Especially because it's a fairly easy sin to keep hidden, despite how prevalent it is.  

Too bad other things are easier for churches to attack because they are much less prevalent and aren't quite so easy to hide.  I don't know of too many churches that openly say fornication is okay, but they sure don't go out of their way to condemn it either when other stuff is available to condemn.  Is it because too many church members would be offended that a sin they're much more likely to be committing is being called out?  Is it easier to simply pick on sins that they have no possibility of engaging in?  If that's the case, I can't imagine God being pleased with that.

I doubt that God is okay with rampant and uncommitted sleeping around, regardless of one's orientation.  As far as I know he has never been okay with it, and has always favored lifetime commitment in intimate relationships.  

Charles Steinmetz - A Guy You Probably Don't Know

I found out about a guy named Charles Steinmetz asking AI a question once.  I believe I asked who it was that first applied imaginary numbers to electrical engineering.  Very interesting.  It sounds like he's just one of the long list of many guys who profoundly influenced society in ways that most of us will never know.  It's a byproduct of specialization and industrialization I guess.  We can't all know the intimate details of every contribution in every field.

I've seen early group pictures of electrical engineers and Mr. Steinmetz stands out the most.  Even more than Albert Einstein in those pictures in terms of appearance.  It's because he had dwarfism.  It's nice to know that he was still able to receive recognition for his contributions even in those early days where prejudices against a perceived norm were a lot more rampant.  It seems he got in trouble more for his political beliefs than his physical stature.  From the miniscule bit I've read about him, I probably would have disagreed with him on some of those beliefs too.

Lawrence of Arabia, The Land of Oz, and the Insufficiency of Ideals

One of the really fun Rifftrax episodes is The Wonderful Land of Oz directed by Barry Mahon https://www.youtube.com/watch?v=4EgY_Tzfn8g.  It's an awful film based on a book that was the first of many sequels written by the original Wizard of Oz author to the original Wizard of Oz book.  

A major plot point in the both the book and film is a young girl named General Jinjur leads a bunch of other young girls in overthrowing the Emerald City because they're tired of tedious chores like homework and babysitting.  But after their success, they run into problems they didn't expect.  None of the girls ever learned how to cook, so they have no food to eat.

Now we go from a very badly produced film to its exact opposite in Lawrence of Arabia, which is probably the longest movie I ever watched.  It was so long it took me two nights to watch it.  And I will probably never watch it again.  But I remember one thing from it quite vividly.  I remember the faction Lawrence fought so hard for struggling to build and maintain its infrastructure on its own, and British officials coming in and being outraged at how badly things like hospitals were being run.

So we see a commonality here.  You can be mad at how things are and fight against them and win, but what about the aftermath?  Can you do a better job overall than the group you're overthrowing?  If you can't, then what's the point?  Having decent ideals is good and all, but that alone isn't sufficient to run a government.  Just like being angry isn't enough to win a fight or pick up a heavy deadlift.  You have to have some sort of knowledge or experience and be willing to develop skills in more than just what you want to fight against.  It really is a tall order.  Not for the faint of heart.

Fraud Triangle Comparison to Sin Triangle

In one of my accounting classes, we learned about something called the fraud triangle, which I thought was a great theory.  It said for someone to execute fraud, they had to have all three of the following:

1) Incentive

2) Opportunity

3) Rationalization

So if someone wanted to steal, but never had the chance to, it wouldn't happen.  Or if they had a chance to, but couldn't make their conscience accept it as a viable option, it also wouldn't happen.  And of course, if they didn't want to, they wouldn't even pursue it to begin with.

Perhaps it wouldn't be a bad idea to put this triangle idea in Bible classes as a constructive theory behind the concept of sin.  I've always felt that Biblical doctrine was a great way to provide the rationalization necessary to protect against the act of committing a sin, even when there was both the opportunity and a desire to engage in it.

A sin triangle also works because sin looks like a trigonometric function to begin with.

New National Anthem?

If we ever get a chance to select a new national anthem, I'd vote for Hulk Hogan's Real American entrance music when he was in the WWF that was performed by Rick Derringer.  I listened to it countless times over the years watching old wrestling tapes and YouTube videos, and to this day I still feel a sense of pride in the country when I hear it, and visualize the great land that America was always intended to be, where righteousness for all is consistently pursued.

 https://www.youtube.com/watch?v=9lZDgGr1PO0&list=RD9lZDgGr1PO0&start_radio=1

https://www.youtube.com/watch?v=sPO5lbFnulE&list=OLAK5uy_keN9V6A6Txc98L-QGKWnCohmOTHLHkycU&index=11

Desire Idea

I had a thought this morning:

Perhaps the people that desire capitalism the most are the ones that deserve it the least, and perhaps the people that desire socialism the most are the ones that deserve it the least.

And I wouldn't be surprised if this desire idea could be generalized to other things as well.

Personally, I'd like to believe that I could accomplish whatever goals I have under either political system.

Serving in Heaven vs. Ruling in Hell

Paradise Lost brings up this debate.  Some would rather rule over chaos than serve under order, and others the opposite.  And for a while I wondered which I preferred.  Then I thought of a scenario that puts this into perspective.  

When I used to compete in lifting meets, I definitely preferred others to be weaker than me.  I'd rather be 1st place with a low combined weight total than 6th place with a much higher total.  Didn't matter if I squatted 315 pounds in the 181 pound weight class, as long as no one else exceeded me. Squatting 700 pounds and being 3rd place just wasn't as good of a prize in my eyes.

And I thought the same initially with regards to intellect.  If I was the smartest in the room, it didn't matter if everyone else WAY below me or just slightly below me.  As long as I was at the top and recognized as the best.

But years later my perspective has changed a bit.  I realized if I was the smartest person ever on earth, the quality of our daily appliances we take for granted would probably be dramatically lower.  Is it worth a lower quality of life for everyone else just to satisfy my own ego?  Can I handle having a lower ranking on the totem pole of recognition if it means a better life for everybody in general?

And it made me realize that it probably is better for me to accept a lower status of governance than to possess total authority over things of inferior quality.  Letting go of a little bit of control can make things go a long way.  And ruling over a bunch of idiots doesn't sound like such a good prize anymore.  Better for us to try to build up those underneath us and accept the benefits of them overtaking us.  

But of course, if those underneath don't want to build themselves up, they are probably better off learning to accept their place.

I Planned a Return at Age Forty - Didn't Happen

I started another blog a few months back called Zen in the Art of Being a Jerk (https://zenintheartofbeingajerk.blogspot.com/), where I talk about how much I like heel wrestling characters.  One of the typical heel characters is often referred to as the closet champion.  This is the champion that refuses to face all challengers, and ducks as many as he can in order to try to artificially increase the length of his often undeserved title reign.

In that spirit, when I was a powerlifter in college, I legitimately feared competing in the very difficult open division.  I was able to compete in the teen division, the junior division, and the collegiate division, and it was much easier to place in those specialized divisions than it was in the open division.  But after college, the number of specialized divisions is slim pickings, and lifters are pretty much forced to compete in the open division.  It isn't until age 40 that you can compete in a masters division for older lifters.  So before I graduated, I joked to my college buddies saying I would avoid competing after college and wait until I'm 40 years old to compete again.

Now at age 44, I'm just too beat up to be anything near competitive.  My digestive issues are the main thing, but my hip flexors bother me on squats too, and last time I tried heavy bicep curls my hand was numb for darn near a month.  I simply can't push myself hard when training anymore without risking injury.  Sure, I could still sign up and lift super low weights in a competition, but that's just no fun.  I guess some guys can keep going strong at that age, but not me.  My back injury in my 20's sealed the deal, and once that finally cleared up a few years later, all my muscle was gone, I had just started a family, and I simply didn't have enough incentive to return.  Then when those digestive issues set in after I hit my late 30's, it was very clear that my competition days were over, never to return.

3rd Grade News

I always like how Trump called the news the Fake News.  Because in some ways he's kind of correct.  I understand not everyone in the population has the mental capacity to read very much (or the free time or interest for that matter), but the choice of articles, and the choice of headlines in particular, are often quite abysmal in order to generate clicks.  They really do seem to be intended, not always to be false as Trump implies, but always to be FAR over-simplified to little more than a catchy slogan that leaves a whole lot of relevant facts out of the account.  Both the left wing and right wing media are very guilty of this.  Probably not EVERY piece of media has this fault, like local newspapers for instance, but online stuff like Yahoo news and the articles it links to often fit this description to a T.  Fox news probably as well, although I haven't paid attention to them in a while.  But I remember in the past they'd take small sound bytes from speeches, ignore the rest, and run with the sound bytes as if those alone said as much as a dissertation.  That is not good journalism.

So I think I'd rather call it 3rd Grade News than Fake News, because it simplifies things too much, where maybe some of the facts are accurate, but they leave out a lot of relevant information to paint a false impression.  I think Lisa Simpson said it best when she said, "As usual, the playground gets the facts right, but misses the point entirely."

I guess the news does what it can to generate revenue and keep afloat.  I know I sure as heck don't like to think deeply about politics much in my time away from work, and I don't blame anyone else for not wanting to either.

I Usually Vote Republican, But Understand Why Many People Don't

I believe in the last general election I voted in, I chose one Democrat, and everyone else I chose on the ticket was Republican.  

As much as I dislike progressivism, I can't deny that there are some things moderate and even staunch Democrats stand for that have genuine merit.  Showing concern for the environment and making sensible efforts to control pollution is certainly not a bad idea.  Showing compassion for refugees attempting to escape from an oppressive government to start a new, honest life looks like the right thing to do as well.  Increasing the tax burden on those who have benefitted greatly from living here and can easily afford the increased burden is difficult to argue against too.  So I certainly understand why people often vote against Republican stances and don't blame them for doing so.  Particularly when economic conditions for the general population are not doing so well under the Republican watch and when a rude fellow with a questionable record and a lot of inherited money is put in charge of the land.

In fact, most of the time I vote, it isn't because I love the Republican stances at all.  I just can't stand the progressive stances.  The ones that look for fault in every darn thing and refuse to be satisfied.  They rarely give those that they are against a clean slate and a chance to start over.  In their eyes, America is forever a land of bigots and will always be racist, sexist, xenophobic, and whatever accusation you want to throw against it - because it was without a doubt a major part of the Atlantic slave trade hundreds of years ago - long before its birth and all the way until the mid 1800's.  

Now, SHOULD progressives hate America forever because of this glaringly awful part of its history?  Don't they have a point?  Maybe so.  But man, if you're going to hate a country, or anything else, that much - you know, FOREVER, no matter what it does in the future - then just don't even be a part of it.  Go to Europe (even though it doesn't have anywhere close to a clean slate as far as its history of human rights goes), or start your own country.  It makes no sense to hate something so much that it can't ever redeem itself, yet to still stay associated with it.  

So until the forever unsatisfied progressives exit the picture, it will be difficult for me to consider lending my support to anyone - even a moderate - who fails to strongly differentiate himself from such a negative and hopeless group that prides itself on unachievable yearnings.  Even if you give this progressive group everything it wants, that's still not good enough because it cannot erase the past.  And the best way to deal with anyone who can't be satisfied with anything you ever do going forward is to simply ignore them.  Why waste effort to appease those who can never be appeased?  

But American progressives do not have to stay in this forever-unsatisfied purgatory.  They can climb out if they so wish without sacrificing much, if any, of their push for improved human conditions.  I think they just need to realize that a big part of changing the future is to accept that the past cannot be changed and to go from there.

That said, do I blame people for picking permanent America-hating sympathizers over convicted felon Trump?  Do I blame people for picking convicted felon Trump over permanent America-hating sympathizers?  No.  I don't blame either one.  Why?  Because some decisions are tough and prioritizing can be difficult. 

Trump is really doing the exact same thing I would do if I was in his position regarding the progressive extremists.  He's completely ignoring them, and even going actively against them.  I have never seen a politician before him have enough brash guts to do that.  So that's one thing about the man I can admire and support, even if his personal life isn't much different than Bill Clinton's.  It really does get exhausting seeing moderate politicians trying to appease the unappeasable, which I witnessed for many years.  FAR too long.

Bart vs. the Space Mutants vs. the Fundamental Theorem of Calculus

Bart vs. the Space Mutants was an insanely hard game on the old 8-bit NES Nintendo system.  I think anyone that played it before knows it.  It's harder than proving the fundamental theorem of calculus. You know how I know this?  It's because I took a Real Analysis course in college where we did actually prove the fundamental theorem of calculus, and I got a B in that course.  But I NEVER could beat Bart vs. the Space Mutants.  Not as a kid or an adult.  The furthest I got was level 4.

Of course that game isn't even the hardest one on the NES.  There were a lot of games on that system I never could beat.  Never could beat Teenage Mutant Ninja Turtles on there either.  Or Beetlejuice.  Or Home Alone.  Or Addams Family.

The hardest games I actually COULD beat were Mike Tyson's Punch Out and Adventures in the Magic Kingdom.  The Magic Kingdom one wasn't quite as bad once I figured out what the stars were for and how I could use them as powerups, and how to use the candle in the pirate level.  But even then it was no picnic.  Space Mountain was still pretty tough to me.

Those old NES games sure were tough.  Especially since a lot of them didn't have any kind of save feature.  Heck, a lot of times you were lucky to even get a password.  Some of the games I could beat with a Game Genie, but of course since it's cheating, that doesn't count.  Some of them I STILL couldn't beat even with a Game Genie.

A Chekhov's Gun Critique

The philosophy behind Chekhov's gun makes sense on the surface, where you don't put something in a story unless it comes up later, but I think there's an interesting technique that I've seen in the Sherlock Holmes short stories where stuff doesn't come up later, but still kind of serves a purpose.  

Often Watson will reference other cases at the beginning of a story, some of which actually appear as short stories themselves and some of which never make it to print.  You may ask, "What's the point of even mentioning the case if it will never come up again?"  And my answer to that would be that it makes the world appear much larger than what we actually see.

Pleasantville 2

To the best of my knowledge, there has never been any kind of sequel planned to the movie Pleasantville.  But I sure love that movie.  Grew up watching Nick at Nite in the early 90's, and so it reminds me a lot of that channel.  

I imagine the sequel would be the citizens of Pleasantville slowly realizing  more and more of the problems that come with open-mindedness that encounters no resistance.  Things like struggling single parent prevalence, profane language dominating entertainment media, addiction to technology, etc.  And then they'd slowly become more open to some of the ideas behind self restraint again.  

And when some small behavior exemplifying restraint is accomplished, a small part of the world would lose its color and return to black-and-white.  Even though not everything would return to what it once was as far as culture and behavioral customs go (racial integration in particular would remain), enough things would revert so that eventually the entire world would turn black-and-white again, slowly biding its time over the years before it becomes open to introducing color and a spirit of open-mindedness once more.  

So it's kind of like a reversal of the main idea of the first film, which focused on the problems with restraint and how the world became more colorful when restraint was cast aside.

I like this idea because it shows that to everything there's a season.  There are seasons of opening up and there are seasons of restraint.  Pros and cons to both.  Open up some, step back a bit, open up some, step back a bit, and keep the pattern going.  The cycle repeats, probably indefinitely.  I believe there are historical examples of this cycle in the past, but at least for the time being, there does not seem to be a prevalence in literature of periods of voluntary self restraint dominating a culture.  Temperance movements have popped up here and there against alcohol, but that's all I'm aware of.

The Trolley Problem in Star Trek TNG

I believe a Reddit forum somewhere discussed this, but I didn't want to participate in a conversation there, so I'll just post a little bit about it here.

Counselor Troi is studying to get the credentials to potentially move up to a captain's position.  But she keeps failing a simulation section of the exam Riker gives her, and he won't tell her why.  Eventually she discovers on her own that the reason she kept failing was because she kept the well-being of each individual person in mind, even when the health of the entire ship was on the line.  

She finally realizes her first duty is to the ship, and so when she next takes the exam, she orders the simulation of LaForge to go in and fix a warp core breach, despite knowing it was going to kill him.  That time she passed the section.

At that point, she realized she didn't want to be a captain anymore.

So the solution to this problem really depends on the duty of the decision maker.  It may mean actively ordering someone to their death if it saves the ship, or perhaps actively sending three our four ensigns to their deaths if it saves the captain and first officer.  Whatever is optimal to keep the ship afloat on its mission is key.  Even if it's not pleasant to think about.  Being an effective leader requires tough and unfair decision making sometimes and it's certainly not for everyone.  I know I often avoid assuming such a position when I can.

Functioning Under Unideal Conditions

Being able to still keep going when things aren't ideal is a crucial skill, because reality is almost never ideal.  I call this ability Functioning Under Unideal Conditions.  If turning it into an acronym that looks vaguely filthy helps you remember it, I guess that's okay.  As long as you can live by the main idea behind it.

Sometimes conditions are so bad that you aren't able to function no matter how tough you are, but if conditions are just unideal, then yeah, it's something you should be able to live with.  You have to shoot for optimal conditions most of the time because ideal is most likely too elusive.

My Unexciting Religious Testimony

I talk about religion a lot in this blog, but I don't think I've ever posted all that much on how I became religious myself.

A lot of people have very dramatic conversion stories, often about how they went down the wrong road and reached rock bottom before finally abandoning shallow pursuits and grasping a much deeper meaning of life.  I am not one of those people.  I grew up with a very religious father, and he grew up in a very religious Louisiana family.  My dad and his seven siblings were very poor growing up, but they all got along really well for as long as I've known them, even now as their days are beginning to end and they're slowly beginning to pass away.

In my elementary school days I was fairly typical.  Did bad stuff every once in a while that got me in trouble.  I'd go to church with my dad here and there and he got me a kid's Bible by Mary Batchelor with great illustrations that I'd look at from time to time without actually reading much.  Most of the time I just watched TV and played Nintendo when I wasn't in school.

One of my many cousins and I were out in the woods of Louisiana one day during this time, and even though his father was a minister, he and I spent that day saying every foul word we knew of at that time, because a bunch we still didn't know.  But then we decided we were tired of that foolishness and pretty much stopped saying bad words after that.

So when I got to middle school and high school I was actually a bit more behaved.  I never had an urge to drink or smoke or anything like that.  Adult magazines and websites were a different story and once I got into those I didn't shake that habit until I was 26 or so.  Other than that I didn't have too many problems other than being very lazy in 10th grade.  But by 11th grade I woke up and stopped being quite so lazy, and life got a bit easier after that.

I believe it was in 8th grade when I finally felt called to walk up to the front of the service during the church's period of invitation and publicly commit myself to following Jesus and his teachings.  I thought about it for a good long while before I finally did.  I think I was worried about not being saved at that point.  I was baptized shortly afterward.  I started going to church regularly, but I got kind of freaked out in Sunday school with the pop religious music and socializing so I pretty much stayed in regular church.  

I read the Bible (or at least most of it) when I went to college, but even by then I didn't feel the spirit impacting me very deeply.  Not that I craved the spirit very much.  Some other religious folks there met me from time to time, but I couldn't be as committed as they were.  I think it was good to meet them here and there and I did appreciate it.  I went to church only sporadically during my college days.

My mom passed away while I was in college and I ended up moving back in with my dad and going back to the church I grew up in and was baptized in.  They asked me to do some of the sound and/or projector and I did it for a few years, but it wasn't very fun for me.  I can't call it a thankless job because I was thanked quite often by many members of the congregation.  I had a lot more fun going to lunch with the medical students after church.  We had a whole Sunday school class of just married medical students at that time because the church is close to a medical school.

A few years later I got married myself ,and my wife and I went to about two or three different churches before picking one to settle with.  I think it was at this time that I finally really started to get a feel of what Biblical doctrine was truly about, and I actually began craving a lifestyle that did not forsake the Lord.  I realized the deep truths of Proverbs and how material as old as that really can apply so much even today.  It's a book I feel EVERY young man should read because all of the pitfalls it talks about are very real.  I realized I couldn't do things on my own and needed the Lord's forgiveness for my shortcomings.  And I came to feel more and more that life is not a meaningless and random series of pointless events.  There's very much an intent behind nature, and MUCH more to the world than meets the eye.

I ended up going back to church with my dad again a few years later, and I guess I've been going with him every Sunday for the past three or four years.  It's a time I cherish because I know it's becoming limited as he progresses to an advanced age.  

Me being middle aged now myself makes me realize how fragile humanity is and how it really does need a lot of help in its battle against sin.  I know I'll take what help I can get because I certainly am not immune from falling into the traps of self-deception and failing to realize my own sins.   That doesn't go away just because I'm a bit older.  I don't care if people think I use religion as a crutch.  Why?  Because I do.  And I don't care if they think I was indoctrinated either.  So what if I was?

My life, even if it seems dull to many, has been quite fulfilling to me, where I got to live many dreams and ambitions and experienced a lot of good fortune.  There were some setbacks here and there and I'm sure those will continue.  But I hope I can be as thankful for all that God has given me as I have been over the past few years of slow spiritual awakening and realizing how amazingly frequently involved God has been in just my mediocre life.  God revealed so very much to me in my secular and religious studies and in my relationships that he never had to show me at all.  But he wanted to anyway.

Even just quiet mornings where I wake up early and take it slow before work bring me so much joy.  I don't even have my heart set on eternal life all that much because I've already been so blessed with just the temporary one God has given me.  Of course I still believe that next life is still there.  But even without it, God's goodness to me here has been so evident.  I know it hasn't been that way for everyone, and those I pray he takes special care of in the next life.

A Bad Idea About Strength

It's probably a bad idea to demand that people who are stronger than you should be even stronger than they already are.  Seems like it could potentially backfire.  

We can't forget that in this world even the strong are more fragile than they appear.

Does the Omniscient Viewpoint Matter?

Here again I'm arguing against moral relativism because it's something I like to do.  Perhaps someone has used this argument before and I've just never seen it.

Suppose we have a court case, and the man is found guilty by the jury because the evidence is compelling and strong.  But also suppose the man is innocent despite the indication of the evidence (kind of like a Sherlock Holmes story).  The jury just voted him guilty because of their limited perception, but really did their best given their lack of omniscience.  You can't bash their integrity for doing what they could with the tools they had.

Now moral relativists would classify the man on trial as immoral because his moral status was determined by consensus after some due diligence.  Even more so if the general public pretty much agrees with the verdict.  But what about the omniscient viewpoint - you know, the only one that can even potentially detect his innocence?  Does that viewpoint mean anything?

We Can’t Say Something Positive is Impossible???

I’ve spent some time lately looking at Godel’s ontological proof and trying to comprehend it the best way I can.  Axiom 5 seems the most troubling to me out of the whole argument, but today I want to focus on just Theorem 1 of the proof and the two axioms leading up to it.  Here it is below, copied from Wikipedia for quick reference:

Theorem 1 says if a property is positive, then it’s possible there exists such a property.  That seems reasonable.  Positive things do exist in this world after all.  But if we look a little more deeply at this statement, this claim is a bit stronger than it looks, because we’re saying we cannot definitively claim ANY positive property is completely impossible in all potential worlds.  We can’t call any positive activity completely impossible.

And Godel seems to use a slick method to claim this, using the vacuous truth rules, which I’m always suspicious of because I think they were just made to keep the truth value system closed to two values instead of opening up a third undecided value.  

First Godel assumes Theorem 1 isn’t true in an attempt to derive a contradiction.  He says “Phi is a positive property AND it’s necessary that for all x, NOT phi of x,” which is the opposite of what Theorem 1 says.  This makes sense.  To negate an if-then statement you assert the premise and the opposite of the conclusion. 

After that he notices that the portion of Axiom 1 stating “it’s necessary that for all x, phi of x” opposes a portion of his assumption.  Plus this portion of Axiom 1 is the beginning of a conditional.  So his assumption to start the proof of the theorem creates a vacuous truth in Axiom 1 where the axiom claims phi of x.  Because of this, by the rules of vacuous truths, the if phi of x then psi of x statement in Axiom 1 is ALWAYS true, no matter what value psi of x takes.

So Godel just takes that psi of x and makes it equal negative phi of x.  So the output of Axiom 1 after this substitution says if (phi is a positive property) and (it’s necessary that for all x, if phi of x then NOT phi of x) then NOT phi is a positive property.  Kind of a nasty double conditional.  The conditional inside the conditional was a vacuous truth.  But the outer conditional has its premise consisting of two true statements, one being phi is a positive property, which we already asserted as soon as we started the proof by contradiction, and the vacuous truth.  So both parts of the conditional premise being true will indeed yield the result of NOT phi being a positive property being a true statement.

All that mess is not easy to write out.  And we did it all just to get the statement “NOT phi is a positive property.”  Now we can finally go to Axiom 2, and claim that since NOT phi is a positive property, then that implies phi is NOT a positive property.  Easy enough.

And of course now we have just concluded phi is NOT a positive property, even though the very first thing we did at the beginning of proof by contradiction was to assume “Phi is a positive property AND it’s necessary that for all x, NOT phi of x.”  So we have phi being a positive property and phi NOT being a positive property.  This is a contradiction, and completes our proof by contradiction.  We have shown that if phi is a positive property then it’s possible there exists some x with that property.

But of course I am very suspicious of a vacuous truth being used.  So I asked my Gemini app if it could produce an example of a similar scenario where this proof structure is followed, and the axioms seem reasonable, but the conclusion seems like nonsense.  Mostly as an attempt to discredit the use of vacuous truths in proofs in the future.  It cleverly suggested to plug in the phi variable as “impossible crime” and the P variable as “legal.”  It also suggested phi as invisible socks and P as fashionable, and phi as boiling ice cream and P as delicious.  These seem CLOSE to fitting the axioms, but I still don’t feel they fit the axioms comfortably enough to my satisfaction when I sit down and try to plug them in.

So even though I don’t like vacuous truth arguments, I can’t seem to invalidate them the way I’d like to.  Perhaps we really do have to admit that if something is positive, then it can't be impossible, at least under the two seemingly reasonable axioms Godel used.  I really have to admire his skill in coming up with this trick.  It’s ugly, and questionable, but I can’t find a way to attack it the way I’d like to, try as I may.  Maybe someone else will have better luck.  

A pretty picture involving the Gaussian Integral

The Gaussian integral is a neat and very easy representation of the bell curve with the area under the curve exactly equal to the square root of pi.  Nice simple-looking expression.  The usual bell curve formula looks a lot worse since it's a family of curves and it also sets the area under the curve equal to one instead of the square root of pi.  Or something of that nature.

Inspired by that expression, I used Desmos to plot the picture below.  The darker shape is just a semi-circle with radius equal to the fraction one over the 4th root of pi.  But I designed the plot so that the dark semi-circle area in the picture was EXACTLY equal to the light orange area between the semi-circle and the bell curve.  I think that precise relationship makes a geometric picture such as this look quite nice, even though it's difficult to intuitively tell the areas are indeed equivalent.  The picture kind of looks like a pretty sunset if you fill it in with the right colors.  Both areas should be equal to the square root of pi over two if I didn't make any errors.

And here are the expressions I typed into Desmos to generate the aesthetically pleasing plots shown above.

I think that's enough fun for one day.

Why is the number e in the bell curve equation?

When I think of bell curves, I tend to think more of Galton boards than a graphical representation of test score averages.  Galton boards are those fun things with all the marbles in them that you flip over and most of them gather in the middle while a few go off to the sides.  Big enough Galton boards can approximate a bell curve fairly accurately.  Really interesting seeing how even though each ball follows an unpredictable path, altogether they form a shape that's quite predictable, if you have enough of them.

Anyhow, Galton boards have binomial coefficients in their mathematical calculations - like many things in probability do - and of course binomial coefficients have factorials.  But what's interesting is factorials can be represented by Striling's approximation.  This estimates n factorial to be pretty close to (root (2*pi*n))*(n/e)^n.  Hopefully I typed all that out correctly, but I'm sure it's not hard to find online.  

Well anyhow, that's how we see an e appear, if we trust formulas like that and feel comfortable looking up the derivations of those formulas later.  Stirling's approximation is involved in the approximation of a factorial, and if you plug those approximations into the binomial coefficients in the formulas similar to Galton board type models, you get a formula called the De Moivre-Laplace Theorem.  

The Galton board shows how a large accumulation of randomized left-right choices from a centralized point (which I guess we could think of as a mean) forms a bell curve, and the De Moivre-Laplace theorem gives the formula showing the e in that equation.

A Look at Why Anti-Derivatives May be Tougher than Derivatives

 The definition of the derivative is the limit as x goes to zero of (F(x+dx)-F(x))/dx.  If you're given a function, it's not too bad to plug it into this thing, do some algebra, take the limit, and see what happens.

But try going backwards.  Try taking a function, then doing algebraic manipulations to get another function into this form.  Seems to be much tougher, and I guess there are a lot more potential options you could do, but then getting them to simplify in the right way seems somewhat daunting if you're like me and not all that great at algebraic manipulation.

Let's take something simple like 2x for example, and try getting its anti-derivative by algebraically manipulating it to look like something that fits the definition of the derivative.

2x

First let's add dx to it.  Since dx will just be going to zero when the limit is taken, I guess it's kind of like adding zero.

2x+dx

Then multiply by 1, but put 1 in the form of dx over dx.

(2x+dx)(dx/dx)

Multiply the top dx through.

(2xdx+dx^2)/dx

Add zero to the numerator, with zero in the form of x squared minus itself.

(2xdx+dx^2+x^2 – x^2)/dx

Shift one of the x squareds to the front.

(x^2+2xdx+dx^2 – x^2)/dx

Realize the first three terms can combine.

((x+dx)^2 – x^2)/dx

Then realize that we now have the function x^2 in the form of the limit as x goes to zero of (F(x+dx)-F(x))/dx.

This implies that the derivative of x^2 is 2x, which means the anti-derivative of 2x is x^2.

That was a LOT of algebraic manipulation I would have NEVER thought of doing if I didn't do this problem backwards to begin with.  And this is one of the easiest anti-derivatives.  Imagine if we tried something harder.

When the tool is more interesting than the thing it was designed for....

I remember learning cursive handwriting in 3rd grade and being very excited about whatever letter I was going to learn next.  It seems obvious to me that cursive was designed to be faster than print since you don't have to lift your pen, but now that computers have taken over, the advantage of speed that cursive writing once had has now become moot.  

The capital G in particular is one of my favorite cursive letters I think.  It's just pretty to look at.  And cursive in general is pretty I think.  While it was designed for speed, now it seems to be more elegant than anything else.  It kind of seems fun to think about printing cursive G's on that old gray multi-lined handwriting practice paper for a day, even though it would serve no practical purpose.  

So the tool once used for enhancing communication speed (cursive) seems more interesting to me than the ability to print a message quickly.  The yanghaiying YouTube channel, with its sporadic focus on Chinese calligraphy, kind of reminds me of the elegance of cursive writing.

Moving on, I know some mathematics was developed as a tool for engineering or some other related field, and other mathematics was developed for its own sake, but often I feel that mathematical tools are more interesting than whatever they were designed to accomplish.  I know very little about Fourier series for instance, but it's my understanding their initial function was to deal with heat equations.  The 3Blue1Brown YouTube channel instead focuses on how they can be used to draw pictures with circles.

Betaine HCL Testimony

Even though I prefer religious testimonies to testimonies about non-religious experiences, I think my particular experience here is worth mentioning - particularly to anyone struggling with chronic severe indigestion.  

I had testicular cancer way back in 2007 and radiation was part of the recommended preventative treatment so it wouldn't spread to other organs.  That radiation was no joke and I had to take STRONG anti-nausea medication in order to function during that time.

Many years later, in 2019, I began to have major digestive issues.  Constant, constant belching and bloating.  Massive indigestion.  Significant weight loss as well.  An endoscopy revealed no definite cause.  Slight gastritis, but nothing else.  At least it seemed to rule out anything big and noticeable like cancer again.  Whether what I was having was caused by or related to the radiation treatment many years before, I have no idea.

Eventually through strong persuasion by good friends that left me no excuses, I tried an unconventional approach with a chiropractor who had a simple test to measure stomach acid.  This was in 2024.  He determined that my stomach acid was very low and prescribed Betaine HCL pills.  These were supplements that provided additional stomach acid when the stomach acid I made naturally fell short.  

I started out taking as few of these pills as possible because I was scared to death of them.  I thought they'd eventually eat a hole through my stomach and kill me.  I suppose that's still a possibility, but now I usually take 15 of them a day (5 per meal), which is the maximum amount the chiropractor recommended, and think nothing of it.  And they certainly make me feel a lot better.  I still bloat up here and there when I eat a little too much, but it's not CONSTANT like it was before I took the medicine.  

So even though we see a seemingly endless amount of antacid commercials for heartburn on TV, I guess some people have the opposite problem and need MORE stomach acid.  I must be one of the few that fall into that category.  

Atlanta Nights

Atlanta Nights is one of the worst books ever.  A bunch of science fiction writers got together to write the worst book they could and trick a self-publishing company into accepting it, and their plan actually worked.  

I may be the only person in the history of the world to read this book from beginning to end TWICE.

Even the people that WROTE the book probably didn't fully read it through once.  They wrote it with each writer taking a separate chapter I believe.

I reviewed it on Amazon many years ago.  But I don't think my review stressed how filthy the book was.  I mentioned it, but didn't stress it enough.  I remember a scene that was quite disturbing involving body parts stored in a room.  Private body parts too.  The book really went out of its way to be tasteless.  

But even with gross stuff like that mixed in here and there it was still quite hilarious for the most part, even during some tasteless scenes.  In one scene, a lady shoots an intruder in her house and then genuinely tries seducing him during his massive blood loss, recognizing him as a former lover after firing her gun.  Pitiful.  

The typos were by far my favorite part.  One guy in one chapter kept rubbing his beard and pushing back his hair.  But "back" was spelled "backs."  So it was a typo.  Only this was written like six times in the chapter.  With the SAME typo every single time.  Also there was one part in that same chapter where someone was told to back off.  But the same typo was present there as well, so it read, "Backs off, you!"  Intentionally hilarious.

Why 26 is a Special Number

I found out a while back that the number 26 is the ONLY number out of all the natural numbers that is immediately after a perfect square and immediately before a perfect cube.  Indeed, 25 equals 5 squared, and 27 equals 3 cubed.  26 is sandwiched perfectly in-between these.  But how do we know there are no other instances of this anywhere?  If we list out ALL perfect squares and ALL perfect cubes, how do we know that no other number will be exactly 1 before and 1 after anything in the two lists?  That's a whole heck of a lot of numbers to test.  Especially since neither list ever ends.

Our first strategy is to write the equation x^2 + 1 = y^3 - 1 and simplify it to x^2 + 2 = y^3.  Okay, that part seems simple.  But where the heck do we go from here?  I was stuck.  So I went to the math stack exchange website, because it had the question along with several answers.  A link is right here:

https://math.stackexchange.com/questions/874226/y3-x2-2-rightarrow-y-3-27-is-the-only-cube-exceeding-a-square-by

But I couldn't really understand the answers I saw for a long time.  Then after pondering over it for a long while and asking AI questions and stuff, I finally got the main idea.  I tried to post that main idea I had as an answer on the math stack exchange site to supplement the other answers, but it was not well received and was promptly deleted.  Probably because the audience for the site is not comfortable working in imprecise layman terms.  So I'm reposting what was deleted here:

"This is a very interesting question to me, and the path to its answer is even more interesting. Since my formal graduate level education is non-existent in this subject and I'm not comfortable at all with a lot of mathematical jargon, I had to think long and hard to understand the solution, even AFTER looking at the other answers here.

But the simplest way I can communicate the main idea behind the answer to the question is this: while it would be WONDERFUL to get this answer without leaving the domain of the integers, it's pretty darn tough to do. So what you do is you examine a domain that contains all the integers, but is actually LARGER than the integers and you get the solutions there. If you only have one solution in that larger domain, then you're only going to have one or less solutions in the integer domain. That's the main idea.

 

So what you do is you take this equation and look at its solutions in the domain that contains all integers AND all integers with scalar multiples of the square root of negative two added to them.

 

Numbers in this larger domain are of the form a+b(root -2) so rewrite the equation x squared plus 1 equals y cubed minus 1 where both x and y take on this form and then work with the algebra and see what happens. This is pretty much what Adam Hughes already did in his answer - better than I could ever do - but I know I had a hard time even comprehending his answer without understanding the main idea about the larger domains first.

 

For the equation you pose in your question in this a+b(root -2) domain, there's only one answer, and it is an integer, and so there's only one answer in the smaller domain of the integers.

 

This post may seem redundant to those comfortable with the material, but for novices I think it's a vital point to slow down on and emphasize in order to fully comprehend. And to put in plain English with little jargon if possible."

So with that main idea in place we factor the x^2 + 2 in the equation as (x+root(-2))*(x - root(-2)), and we can work in the larger domain.  So x^2 + 2 = y^3  becomes (x+root(-2))*(x - root(-2)) = y^3.

Then we can write the y in the a+b(root(-2)) form and take the cube of that form to see what happens. (a+b(root(-2)))^3 is straight-forward to expand but a lot of effort.  Thankfully the Adam Hughes answer in the site already does that part.  He has a good answer but for people who don't know what norms or integer rings are, they're going to be lost on how to even begin.  I certainly was.

Uncertainty Principles and the Failed Quest for the Worst Movie Ever

When I first started watching Mystery Science Theater 3000 on the Sci-Fi Channel back in 1997, after several black and white movies and a few color ones, all of a sudden episode featuring the film called "The Incredibly Strange Creatures Who Stopped Living and Became Mixed-Up Zombies" sprang up and caught me by surprise.  Sure, the movies before this one were quite laughable, but this one clearly stood out.  I instantly thought it was the worst film I had ever seen and that I ever would see.  But then a few months later "The Horror of Party Beach" shows up.  I still thought Incredibly Strange Creatures was worse, but Party Beach was a major contender.

Over the years I was exposed to more MST3K movies, particularly from earlier seasons, and man there were some bad ones.  I kept looking for one that was clearly the worst.  And titles like "The Wild, Wild World of Batwoman" were pretty much on par with Incredibly Strange Creatures.  Then years later Rifftrax comes along and boy, they really found out how to scrape the very bottom of the barrel.  Santa and the Ice Cream Bunny might have actually been worse than Incredibly Strange Creatures.  And of course later we start seeing titles like Rollergator and Birdemic, and more recently stuff like Suburban Sasquatch and The Amazing Bulk.  This stuff is utter trash.  So much of it could really claim to be tied for first place as the worst movie ever.  But the one that made me truly give up my quest for the worst movie ever in earnest was Fun in Balloonland.

Does that mean Fun in Balloonland is the worst movie ever?  Not really.  My exposure to it simply establishes that finding a movie that's definitively the worst ever is too vague of a question.  IS Fun in Balloonland even a movie?  It's slightly shorter than a full length feature, the credits seem to be limited or non-existent, and half of the movie is clearly just parade footage with no story whatsoever.  Fun in Balloonland is borderline a home video.  So can a home video even qualify as the worst movie ever?  I mean, it's not a real movie in that case.  The worst movie ever is not a movie at all.  So definitions start to break down.  It's like the uncertainty principle in physics.  You try to know momentum and you can't know position, and you try to know position and you can't know momentum.  At least that's how my untrained mind understands the principle.  

And with Balloonland, it's like you try to measure its quality and you sacrifice measuring how close it is to an actual movie, and you try to measure how close it is to an actual movie and you sacrifice how you can measure its quality.  Because you'd judge the quality of home movies differently than you'd judge the quality of regular movies.  At least I'd think you would.

For years I tried to put this uncertainty principle for bad movies into more mathematical terms, proving that attempting one type of measurement always disrupts the other, but have failed in my attempts to do so.  So I guess I've given up proving that there can be no worst movie ever, just like I gave up actively looking for the worst movie ever.  This is what Fun in Balloonland did to me.

Strange Bean Novels From 20 Years Ago

When I first read Alice's Adventures in Wonderland I absolutely loved it.  It was wonderfully goofy and weird, and I thought it would be fun to try to write something like that myself.  So I did.  I wrote the weirdest, goofiest thing I could think of.  Long, long ago.  But I didn't actually post it online until fairly recently.  I guess I delayed it because I thought I'd eventually try to clean it up more and make it better and try to market it again.  But I got too busy with other things and decided I probably wasn't going to work on it anymore and to just leave it as it is.  Especially since the likelihood of publication was slim to none, leaning far more towards none.  

But I had a lot of fun writing it and a lot of fun re-reading it even though it has its flaws.  Hopefully I uploaded it with no sections missing and all the sections in order.

I called this unpublished book Boomo the Bean Visits Confusion Country, and a link to it is here:

https://confusioncountry.blogspot.com/

But after I wrote that one I also wrote a crazy sequel, Boomo the Bean Sees Through the Hourglass, and the link to it is right here:

https://boomohourglass.blogspot.com/

Also, if you click on my blog profile, you'll find the links there as well.  I put illustrations in the books too and that was a big part of the fun.

Causes, Effects, and Natural Selection

Science is about causes happening and effects stemming from those causes.  Goal setting is about changing causes to reach desired effects.  In goal setting you are not observing effects as in science.  You are dictating them.  

Natural selection appears to be a goal to sustain life.  Strict cause and effect should have no goals.  I am not arguing that natural selection is false here.  But I certainly don't mind asserting that nature has intended goals.  There's a term already in existence for this assertion - teleology.  And there's also a term for its counterargument - teleonomy.  

When I asked Copilot AI about teleology, it suggested an argument based in teleonomy that variations in species occur randomly, and environments filter out the variations so that only the successful variations survive.  Sure seems to be more of a deterministic argument than a free will argument.  

But I believe that the striving we experience in life goes far beyond unintentional programming.  Can't prove it of course.  But I can assert it vehemently.    

Obligation vs. Preference

It should seem clear that obligation is not determined by preference.  Certainly not at the individual level because it can potentially erase accountability.  But then we have to think, is obligation determined by collective preference?  I would imagine not.  Otherwise books like Extraordinary Popular Delusions and the Madness of Crowds never would have been written, and peer pressure wouldn't have a negative connotation.  

Why Does EVERYONE Say Their Parents Were Bad?

I don't know if I visit the most representative locations on the internet as far as statistical samples go by frequenting Yahoo news articles and political Youtube videos and such, but I swear, in almost every forum or comment section, for every one person I see complimenting their parents and calling them a blessing, I see about 20 or 30 talking about how toxic their parents were.  And we're not talking about teenagers that are still in the middle of maturing and dealing with discipline issues.  These are people in their 30's and 40's who've had ample time to look back.  

My question is, why the dissatisfaction?  Are there really THAT many bad parents out there abusing and neglecting their kids?  Is there just too much expectation regarding parental roles where they have to be absolutely perfect to even be considered decent?  I mean, WHY do so many people have problems with their parents?  I had awesome parents, so it boggles my mind that so many people apparently did not.  

I can't stress enough that I have NO problems with my parents and what they did in my upbringing whatsoever.  They were good people that tried their very best and did WAY more than they ever should have for me.  Were they flawed human beings?  Of course.  Who isn't.  But once I grew up, and possibly even before then, I could certainly tell that they clearly had my best interests at heart and put in SO much effort and sacrifice for my own wellbeing - particularly my mom.  

This realization is not dampered when I look back and think how scared I was when my mom yelled at me or how mad I was at my dad for using the belt when I got really out of line.  They did these things because I needed correction.  Not because they were on some power trip or thought it was fun.  Because they darn sure didn't seem to have fun correcting me.  Not to mention they bought me more toys than I could even count over those 17 or so years.  And they didn't cheat on each other or spend all night at the bar.  

Are parents like mine really so rare?  If so, I guess I can see why the divorce rate is so high.  But it still boggles my mind that so many parents would be problematic enough to not even be considered decent, much less good.  

Even if I classified mine as phenomenal, that could still potentially be an understatement.  The fact is they deserve more love and respect than I could ever give them.  Thank you mom and dad.  Regardless of how your peers behaved, you were shining examples of a traditional family structure.

Exploring Oppression's Limits... On the Weak End

I wonder, how oppressed would Cinderella consider herself to be if her stepmother and stepsisters still held household authority over her, but forced her to do little or no chores, and she spent most of her time playing on a computer all day.  I imagine if they continued to verbally torment her, that would still be oppressive (or at least abusive).  But I'd think it would take more to claim she was genuinely oppressed besides her not be the one in charge making the decisions.

I think to be a true oppressor, one has to exercise enough authority that they transfer most of the shared workload to the one they're oppressing, and not carry it themselves.  But I'm not sure how much distinction we make between terms like jerk, bully, oppressor, and abuser on a daily basis, and that may factor into this thought exercise here.  Those terms probably each emphasize slightly different negative characteristics.

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

 

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.