How should we feel about Good Friday?

On the one hand, if we love Jesus, we don't want him to be crucified. We can't be happy that an innoncent man suffered that much. But on the other hand, his death bought our salvation. He did it for us. He made peace between us and God.

Jesus' disciples certainly weren't having a good day when Jesus was crucified. But they probably didn't fully understand the significance of his death at that time. In fact, some (maybe all) lost hope. I wonder how they would've felt, though, if they had fully understood what Jesus' death meant.

On the one hand, they would've seen how God was being glorified by Jesus' death. His plan was coming to fruition. It meant not only their salvation, but the salvation of all of those who would believe in him. But on the other hand, they knew Jesus personally. They had a deeply personal emotional connection with Jesus. It must've been horrific for them to see somebody they loved suffer to such a degree, even if it was for their own good.

So how should we feel about Good Friday? I don't know. Maybe it doesn't matter how we should feel. We feel what we feel. At the very least, though, we should be thankful, and we should praise God.

She speaks the truth

Lots of cream and lots of sugar

I don't drink coffee very often, but when I do, I have it with lots of cream and lots of sugar. People sometimes say to me, "You don't actually like coffee. You like cream and sugar." But actually, I can't stand cream and sugar. That's why I put coffee in it.

What is a woman?

The reason this is a funny question is because of how people are defining women these days. They'll say you're a woman if you claim to be a woman, believe you're a woman, etc. If a woman is somebody who claims to be a woman, then what exactly are they claiming to be? Well, if a woman is somebody who claims to be a woman, then somebody who claims to be a woman is a person who claims to be somebody who claims to be a woman. And since that's what they're claiming, then they are basically claiming to be somebody who claims to be somebody who claims to be a woman. Etc. etc.

The gospel in a nutshell

There are parts of the Bible that are so hard to understand, you can spend your life wrestling with them and still not be sure. There are other parts that require a lot of work to understand, but if you have a passion for it, you can figure it out. Then there are other parts that are so obvious there's no excuse for not understanding them.

Thankfully, the most important things are easy and obvious. I'm going to explain, in the simplest terms I can, what I take to be the basic message of the Bible and why it's relevant to you. This is all in summary, so I'm not going to quote scripture.

There is one God whose name is Yahweh. In Hebrew, it looks like this:

Reading from right to left (because that's how Hebrew rolls), the letters are Yod, He, Wah, He, which we transliterate as YHWH, then add vowels to get Yahweh. The King James Version writes it as Jehovah in a few places, but it's the same name. Jews haven't pronounced it in over two thousand years, and since there's no vowels in ancient Hebrew, the correct pronunciation is speculative.

He is the creator and ruler of the cosmos and everything in it. He is a being on which everything else depends, and he's at the top of all authoritative heirarchies. He is a being of absolute perfection. He is all knowing, all powerful, and wholly good.

God imposes moral obligations on all of mankind. There is a real difference between right and wrong. This difference is rooted in God's character and is made manifest in his commands and requirements. He cares how we live our lives. His moral will is revealed in the Bible, but it's also revealed in our own consciences. We all possess an innate sense of right and wrong even if we are sometimes mistaken about the details.

Every one of us violates our moral obligations. Not one of us is morally perfect.

God holds people accountable for how they live their lives. There will be a day of judgment in which we all have to give an account of ourselves to God. We all have to answer to him. God will judge people for everything they said or did, whether good or bad. There will be punishment for the bad things we said or did, and there will be rewards for the good things we said or did.

Jesus of Nazareth is the Messiah, aka the Christ. That means he is an anointed king. Originally, the messiah was thought to be the fulfilment of a promise God made to king David that his dynasty would last forever, and so there would always be a man to sit on the throne of Israel. But Jesus is not only king of Israel; he is king of the whole cosmos. As Christians put it, he is King of Kings and Lord of Lords.

God is three persons--Father, Son, and Holy Spirit. There is one being, but that one being is tri-personal. The Father, Son, and Holy Spirit are distinct persons, but they share the same divine essence. In other words, they are the same being. Jesus is the Son of the Father, which makes him the Son of God. But he is also God.

Although Jesus was God, he humbled himself by taking on the nature of humanity. He was born into the world through a human woman named Mary. He came into the world, not only to reveal God's will through his teachings, but to save people who cannot save themselves. It was out of love and a desire to glorify himself through the demonstration of his mercy that Jesus came into the world. Although Jesus was just as human as the rest of us, he lived a sinless life in perfect obedience to the Father. He is the only human to have ever done so.

Jesus died to atone for our wrong-doing. God is not just a harsh inflexible ruler who is out to get us. Since he is wholly good, his character consists both of justice and of mercy. None of us are morally perfect, and we all stand to face judgment for our moral imperfections, but God has provided a means of obtaining a pardon through Jesus. Jesus paid the penalty we deserve by willingly dying by crucifixion, and his death is sufficient to cover our moral imperfections.

After dying for our sins, Jesus rose physically from the dead. He did not rise back to a normal mortal life. Rather, he rose to immortality. Although it was a physical resurrection, it was also a transformed physicality. His resurrection vindicated his claim that he was the Messiah and that he was sent by God the Father. His resurrection vindicated everything he taught about himself, his kingship, and his mission to save people through his death.

Jesus' death on the cross saves to the uttermost all of those who put their trust in him. If you confess that Jesus is king, and you trust that he died for your sins, you will have eternal life. You will not be judged for your moral failures. You will be pardoned. God will treat you as if you had the same righteousness that Jesus himself had. You will, in a sense, be clothed in the righteousness of Jesus. And just as Jesus was raised to immortality, you too will be raised to immortality. Once you have been raised to immoratlity, you will no longer suffer any pain, sickness, or death.

Once the resurrection and judgment have taken place, those who have put their trust in Jesus will forever bask in the glory of God. We will be able to behold him in a way that we are not able to see him now. We get a glimpse of who God is through reading the scriptures and learning about Jesus, but in eternity, we will come to know him more fully and directly. God will make his dwelling with mankind. We will be able to learn about and appreciate all his glorious attributes, including his love, kindness, power, and every conceivable good thing. We will be forever happy. We will experience love to its fullest extent.

This is the gospel--the good news about what God did to save sinners. People who embrace the gospel (i.e. put their trust in Jesus) do so not only out of self-interest, but out of a love for their creator. To love God is to want to be the kind of people he requires us to be. So it is impossible to honestly embrace the gospel without also wanting to be better people. Primarily, God wants us to love people, and we love people through how we treat them. This includes not only our family and friends, but even people who dislike us or even hate us. We are to love our enemies, remembering that before we knew Jesus, we were enemies of God, and he loved us anyway.

Once we have put our trust in Jesus, we have crossed over from eternal death to eternal life. There is a sense in which we have become new people. God gives us the Holy Spirit as a deposit guaranteeing what is to come. The Holy Spirit dwells in us for the rest of our lives. His indwelling manifests itself in a desire to please God. The result is a life long process of deeper understanding and moral improvement. We will never reach moral perfection in our mortal lifetime, but the desire to be part of God's kingdom will drive us to positive character development.

The indwelling of the Holy Spirit will also give us a hunger for God, to learn about him through reading and studying the scriptures. This desire to be part of the kingdom of God will also manifest itself in a desire to be in communion with our fellow citizens of heaven, i.e. other Christians. Christians gather together in churches to worship God and to learn about him. We strengthen each other throguh mutual edification. We are all gifted in different ways for our mutual benefit. Some are gifted in teaching, some are gifted in helping, some are gifted in encouragement. The Bible lists various ways people are gifted for the sake of mutual benefit, but I suspect it is not exhaustive in listing these gifts. Just by being at church, worshipping together with like-minded people, you encourage those people, strengthen their confidence, given them a sense of belonging, etc. They, in turn, do the same for you.

So I encourage you to put your trust in Jesus. Jesus is God, but that did not stop him from becoming a man and enduring the same things all humans have to endure a result of living in this world. He did so out of love, to save his people. We all have to die, but Jesus came into the world when he didn't have to, and he did so for the purpose of dying so that we might have eternal life. Having defeated death by rising from the dead, Jesus sat at the right hand of the Father and became King of Kings and Lord of Lords. He is a King worthy of honor, respect, gratitude, love, and worship. I encourage you to loves, serve, and trust in the one true King--Jesus.

See also, "The Gospel in Plain Language" on Paul Scott Pruett's blog.

The cosmological "constant" is in trouble again

No long ago, I made a post about the Λ-CDM v. the Timescape models of the universe where I talked about two papers that came out claiming the apparent acceleration of the expansion rate of the universe might be an illusion caused by time dilation due to growing cosmic voids and changing clumpiness over time. This alternate view is called the Timescape model, and it does away with the cosmological constant (Λ) altogether. I found that interesting because Λ is often cited as the most fine-tuned of all the fine-tuned constants, but if Timescape is true, then there is no Λ, much less a fine-tuned one.

Now, Λ faces a new challenge. There's a new paper that came out claiming that Λ isn't a constant after all. It changes over time. It was stronger in the past.

Λ resurfaced over two decades ago when it was discovered that the expansion of the universe is accelerating. Since the cause of the acceleration was unknown, it was called "dark energy." It was assumed, at least, that the accleration was constant. But now, it looks like the accleration hasn't been constant.

Several YouTube science channels have talked about this recently, including Becky, Maggie, and Sabine (EDIT: and now David and Matt). They all discuss the threshold of statistical significance (σ). At this point, the threshold for "definitely a fact" hasn't been met, but I think it's been met for reasonablness. One of them, I think, said it amounted to around a 99% probability, which is good enough for most ordinary people even if it falls short of astrophysics standards.

If Λ is not constant, then it can't very well be a fine-tuned constant. But I don't think that means there isn't some sort of fine-tuning involved. It may just be a fine-tuning of the initial conditions. Or maybe it's a fine-tuning of the second or third derivitive of the expansion rate. In other words, while the rate of acceleration may not be constant, the rate of change of acceleration could be constant. The initial conditions, plus the rate of change of acceleration could both be fine-tuned. I guess we'll have to wait and see.

Does light experience time, and does Hakeem Oluseyi know what he's talking about?

Lately, a bunch of videos have been popping up on my Instagram feed where Neil DeGrass Tyson explains that photons do not experience time. Since learning about special relativity, his reasoning really rubs me the wrong way because it's completely flawed.

Special relativity deals with how things like distance and time differ depending on relative motion between inertial frames of reference. If an object is in an inertial frame, that means it is not experiencing acceleration. While you're sitting on your couch, it may seem that you're not experiencing acceleration since you aren't moving, but you are at least experiencing gravitational acceleration. So you're not actually in an inertial frame. If you were in an inertial frame, you would be experiecing weightlessness.

An object moving at a constant speed and direction (i.e. a constant velocity) is in an inertial frame. That is true regardless of the speed or direction which means there can be multiple inertial frame all in motion relative to each other.

No matter what frame of reference you are in, time will tick at the same rate with respect to yourself. In other words, whether you're moving very fast, very slow, or not at all relative to something else (like the earth), you will not notice a difference in the rate at which time ticks in your frame of reference. However, if an object is moving relative to you, time in its frame of reference will tick at a different rate relative to you. The difference in the rate at which time ticks in different frames of reference is called time dilation.

Let's say you're in an inertial frame, and you're watching something fly by at some fraction of the speed of light relative to you, and you want to know the rate at which time for that object is ticking relative to you. You can calculate it using the formula for time dilation, which is derived from the Lorentz transformation. The equation is:

\[ \normalsize \Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}} \]

See here for an explanation of where this forumula comes from.

Δt is the amount of time that has passed in the frame that is moving relative to you.

Δt' is the amount of time that has passed in your stationary reference frame.

𝑣 is the velocity of the moving frame.

c is the speed of light, which is the same in both frames. This is one of the postulates of special relativity, which will become important in a minute.

Notice that if the "moving" frame isn't moving (i.e. 𝑣 = 0), then Δt = Δt'. In other words, if there's no relative motion between the two inertial frames, time will tick at the same rate in both.

Notice, on the other hand, that the higher the velocity of the moving frame, the smaller the denominator. The smaller the denominator, the larger the whole fraction. Since the fraction is equal to Δt', it follows that the faster an object is moving relative to you, the more time will pass in your frame than in the moving frame. That means time is ticking slower in the moving frame compared to your frame.

Now, imagine what happens when the moving object approaches the speed of light. Notice it can never actually reach the speed of light because if 𝑣 = c, then the denominator = 0, and that don't make no kinda sense. But we can take the limit of Δt' as 𝑣 approaches c. When we do, we discover that Δt' approaches infinity as 𝑣 approaches c. That means in your frame of reference, if something were moving close to the speed of light relative to you, its time would be nearly at a stand still.

Neil thinks that photons don't experience time. His reasoning is that since photons move at the speed of light, it must be that from our point of view, time is not moving at all in the photon's frame of reference.

But there is a huge boo boo in Neil's reasoning. One of the postulates of special relativity is that light has the same speed in all inertial frames. If we imagined an object moving at a constant velocity relative to us, it would have its own inertial frame. It would not be moving in its own inertial frame. But there is no inertial frame for light. There is no frame in which light is not moving. So it's completely meaningless to talk about a photon's inertial frame. A photon does not have an inertial frame. Neil's major boo boo is to treat a photon like an ordinary object in an inertial frame. That's nonsense.

Another mistake is that by treating the photon like an ordinary object moving at the speed of light, and applying the time dilation equation to it, he'd have to be dividing by zero, which doesn't make sense. The time dilation equation shows that an inertial frame can get arbitrarily close to the speed of light, but it can't reach the speed of light. You can't apply the time dilation equation to anything moving at the speed of light, and that includes light itself.

It wasn't long ago that Neil's reasoning would've made sense to me. Thankfully, I've discovered FloatHeadPhysics on YouTube, and he has really helped to straighten out a lot of confusion I was having while trying to understand special relativity. He has one video where he addressed the subject of whether light experiences time. I highly recommend this video because it explains very clearly what's wrong with Neil's reasoning. Neil is simply forgetting the postulates of special relativity.

It just shows to go you that even physicists can get stuff wrong. You have to be especially cautious when it comes to popularizers, and Neil is one of the worst. I saw another video where he butchered the Andromeda Paradox. [EDIT 4/27/2025: I just saw the clip again, and it was actually Neil's guest, Hakeem Oluseyi, who butchered the Andromeda paradox, not Neil. Check out Sabine's take on their error. Also check out Mahesh's video on the Andromeda paradox because it's probably the best video on YouTube on the topic.]

The necessity of targeted proteins

Please forgive me. My brain often operates a 0.5x speed compared to the brains of other people. I can have somebody explain something to me multiple times, and still not understand it. Then, one day, without them adding any more explanation, I'll suddenly understand what they were trying to tell me. It just took me a while to get there.

This morning, I think I finally grasped something Paul Scott Pruett has repeated to me multiple times (see his last comment here for example). Scott has mentioned there and elsewhere that evolution has to target certain specific proteins for things to evolve. When I did my calculations on functional protein probabilities (part 1, part 2, and part 3), I was just trying to figure out what the probability was that the observable universe might, in some way, cough up a protein that could be functional, and I was assuming that whether it could be function was based solely on whether it could fold up into a stable shape.

It seemed to me to be a mistake to run these calculations as if evolution had to target specific proteins since any protein that could fold into a stable shape had the potential of being functional. If you were considering a protein with a length of 150 amino acids, the probability of getting any one specific sequence of amino acids with one random try would be 1 in 20¹⁵⁰, which is pretty low. I thought that was cheating since the real question, as far as potentionally functional proteins were concerned, was what fraction of those 20¹⁵⁰ possible combinations could fold up into stable shapes. It could have been, for all I knew, that half of all the possible sequences could fold into stable shapes and were therefore potentially functional. It turned out to be far less than half (Douglas Axe estimating 1 in 10⁷⁷ while others estimated 1 in 10¹¹), but I still ended up calculating that it's not unlikely at all that the universe would cough up at least one functional protein given the vast probabilistic resources in the universe due to its size and age.

Life requires more than one functional protein, though. Life requires many proteins that work together. Let me use an analogy to explain what I mean. Let's say a protein folds up into the shape of a bolt. To get a nut that fits that bolt, the nut would have to be targeted in some way. It would have to have the right size and have its threads match the threads on the bolt. You might be able to imagine a wide variety of different kinds of bolts, all with different sizes and different thread pitches, but for any particular bolt, the nut that goes with it has to be targeted in specific ways.

In the same way, if proteins are to work together in a machine, they have to somehow fit together. While you may be able to get a random protein that folds into a stable shape, you have to get a targeted protein that "fits" the original protein before you can get anything approximating a machine with different parts that work together. You can't get life just by gathering a collection of stable proteins. Some of the proteins have to be targeted in such a way that they are able to work with or fit together with other proteins.

For a nut to fit a bolt, it has to have the right sized hole and the right thread size, shape, and pitch, but there can be variation elsewhere. It can have an exterior with a hexagon shape or a square shape. It can have a different wall thickness, and it can fit bolts of different lengths. In the same way, it may be that for a given protein to function in a cell, there can be some variation in its companion proteins and still be able to work together. But there are far fewer proteins a given protein can work with than the range of all stable proteins within any given length. That means if we want to grant the existence of some random functional protein, and we want to calculate the probability of getting a simple machine that contains that given functional protein, we are going to have to calculate the probability of some targeted proteins--proteins that "fit" the original given protein.

Since the range of targeted proteins is smaller than the range of stable proteins, it's going to end up being far less probable that life could evolve significantly than it is that the universe could just cough up a stable protein. I think that's what Scott has been trying to tell me.

I don't know how I would even begin to try to run a calculation on this, though. There are too many variables and too many unknowns.

I want to say one more thing Scott said that I think I did kind of understand. The fact that evolution targets certain genes and proteins is evident in the fact that there is convergent evolution, not just on the macro scale (e.g. eyes, sonar, etc.), but also on the micro scale (genes and proteins). I'm not sure whether we should consider this sort of targeting to be unlikely, though. On the one hand, a naturalist could say that since evolution seems to favour certain outcomes, they're not that unlikely after all. We may just lack an explanation of why evolution tends toward certain outcomes. On the other hand, a supernaturalist could say that since convergent evolution is statistically improbable, the fact that it happens over and over favoures an intelligent cause. I don't know who wins that argument. Maybe my brain will eventually catch up on that in the future.

There is always the possibility that I am still misunderstanding Scott about targeted proteins.