This Sanctuary Sunday Open Thread, with full respect to those who worship God on the Sabbath, is a place to reaffirm our worship of our Creator, our Father, our King Eternal.

It is also a place to read, post and discuss news that is worth knowing and sharing. Please post links to any news stories that you use as sources or quote from.

In the QTree, we’re a friendly and civil lot. We encourage free speech and the open exchange and civil discussion of different ideas. Topics aren’t constrained, and sound logic is highly encouraged, all built on a solid foundation of truth and established facts.

We have a policy of mutual respect, shown by civility. Civility encourages discussions, promotes objectivity and rational thought in discourse, and camaraderie in the participants – characteristics we strive toward in our Q Tree community.

Please show respect and consideration for our fellow QTreepers. Before hitting the “post” button, please proofread your post and make sure you’re addressing the issue only, and not trying to confront the poster. Keep to the topic – avoid “you” and “your”. Here in The Q Tree, personal attacks, name calling, ridicule, insults, baiting and other conduct for which a penalty flag would be thrown are VERBOTEN.

In The Q Tree, we’re compatriots, sitting around the campfire, roasting hot dogs, making s’mores and discussing, agreeing, and disagreeing about whatever interests us. This board will remain a home for those who seek respectful conversations.

Please also consider the Guidelines for posting and discussion printed here: https://www.theqtree.com/2019/01/01/dear-maga-open-topic-20190101/

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Wheat . . . Or Weeds?

²⁴ . . . “The kingdom of heaven is like a man who sowed good seed in his field; ²⁵ but while men slept, his enemy came and sowed weeds among the wheat and went his way. ²⁶ But when the grain had sprouted and produced a crop, then the weeds also appeared. ²⁷ So the servants of the owner came and said to him, ‘Sir, did you not sow good seed in your field? How then does it have weeds?’ ²⁸ He said to them, ‘An enemy has done this.’ The servants said to him, ‘Do you want us then to go and gather them up?’ ²⁹ But he said, ‘No, lest while you gather up the weeds you also uproot the wheat with them. ³⁰ Let both grow together until the harvest, and at the time of harvest I will say to the reapers, “First gather together the weeds and bind them in bundles to burn them, but gather the wheat into my barn.” ’ ” (Matthew 13:24-30)

In the agricultural society of Christ’s time, many farmers depended on the quality of their crops. An enemy sowing weeds would have sabotaged a business. The weeds in the parable were likely darnel because that weed, until mature, appears as wheat. What would a wise farmer do in such a dilemma? Instead of tearing out the wheat with the weeds, the landowner in this parable wisely waited until the harvest. After harvesting the whole field, the weeds could be separated and burned. The wheat would be saved in the barn.

In the explanation of parable, Christ declares that He Himself is the sower. He spreads His redeemed seed, true believers, in the field of the world. Through His grace, these Christians bear the fruit of the Spirit (Galatians 5:22-24). Their presence on earth is the reason the “kingdom of heaven” is like the field of the world. When Jesus said, “The kingdom of heaven is at hand” (Matthew 4:17; Mark 3:2), He meant the spiritual realm which exists on earth side by side with the realm of the evil one (1 John 5:19). When the kingdom of heaven comes to its fruition, heaven will be a reality and there will be no “weeds” among the “wheat.” But for now, both good and bad seeds mature in the world.

The enemy in the parable is Satan. In opposition to Jesus Christ, the devil tries to destroy Christ’s work by placing false believers and teachers in the world who lead many astray.

But we are not to pursue such people in an effort to destroy them. For one thing, we don’t know if immature and innocent believers might be injured by our efforts. Further, one has only to look at the Spanish Inquisition, the Crusades, and the reign of “Bloody Mary” in England to see the results of men taking upon themselves the responsibility of separating true believers from false, a task reserved for God alone. Instead of requiring these false believers to be rooted out of the world, and possibly hurting immature believers in the process, Christ allows them to remain until His return. At that time, angels will separate the true from false believers.

In addition, we are not to take it upon ourselves to uproot unbelievers because the difference between true and false believers isn’t always obvious. Weeds, especially in the early stages of growth, resemble wheat. Likewise, a false believer may resemble a true believer. In Matthew 7:22, Jesus warned that many profess faith but do not know Him. Thus, each person should examine his own relationship with Christ (2 Corinthians 13:5). First John is an excellent test of salvation.

Jesus Christ will one day establish true righteousness. After He raptures the true church out of this world, God will pour out His righteous wrath on the world. During that tribulation, He will draw others to saving faith in Jesus Christ. At the end of the tribulation, all unbelievers will be judged for their sin and unbelief; then, they will be removed from God’s presence. True followers of Christ will reign with Him. What a glorious hope for the “wheat”!

*https://www.gotquestions.org/parable-wheat-tares.html

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Glory Train

The track is all clear, the switches are thrown
The Glory Train’s coming; we’re going home
It may be soon or the sweet by and by
We’ll not know the day; so don’t even try

Now, at the station, the platform is full
But all is not quiet; some push, some pull
Many evil men fight to be the king
They want control over everything

Others wait patiently, doing good deeds
Helping those that hurt and in great need
They know the train will be coming for them
And long for peace, not the platform’s mayhem

All ticketholders are ready to leave
They’ll go aboard, all who truly believe
They trusted God and God’s only Son
Marked by God’s Spirit for when the train comes

Life on the platform goes on without end
But one day the train speeds around the bend
Many in the crowd raise a rousing cheer
While others are shocked and cower in fear

The Conductor calls out “Welcome! Come aboard!”
“All you who believe and trust in our Lord!”
“By faith you believed, now God’s Day is come”
“Your race is over, your victory’s won”

Then a strong voice, with trumpet and shout
By God’s Holy Power calls the dead out
They rise from their sleep and all board the train
Wearing bright, white garments, freed from all stain

Then those here waiting respond to the call
Tears flowing freely in wondrous thrall
All climb aboard to their purchased place
Paid for by Christ by God’s mercy and grace

The ones left on the platform weep and wail
They put themselves first, now they know they’ve failed
Their faith was only in the world and man
They fought against God and ignored His plan

Now, without God, they must find their own way
Living in sin until the Judgment Day
When they’ll kneel to Christ, unable to stand
And from God’s presence eternally banned

The doors all close and the train pulls away
Oh, what a glorious sight on that Day!
Up through the clouds in the blink of an eye
Then huge Pearly Gates appear in the sky

Into Heaven’s Realm, we’re nearing our home
Of perfect peace and joy, never to roam
Just over the river, close by the shore
There we’ll debark for our forever more

The train slows and stops, the golden bells ring
What a great welcome as the angels sing!
The old has all gone; we’re changed new and free
All of us sing and shout the victory!

We now have arrived at our Promised Land
With calm, deep blue seas and warm, white sands
And across the river, green fields and hills
With sparkling lakes , so peaceful and still

Oneness fills all, and love that doesn’t cease
And abiding joy, and deep, heartfelt peace
Giving God all the glory and our praise
Throughout all time for Eternity’s days

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On this day and every day –

God is in Control
. . . and His Grace is Sufficient, so . . .
Keep Looking Up

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Hopefully, every Sunday, we can find something here that will build us up a little . . . give us a smile . . . and add some joy or peace, very much needed in all our lives.

“This day is holy to the Lord your God;
do not mourn nor weep.” . . .
“Go your way, eat the fat, drink the sweet,
and send portions to those for whom nothing is prepared;
for this day is holy to our Lord.
Do not sorrow,
for the joy of the Lord is your strength.”

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Not an Eagle

On my way to work there’s a large nest up in a half-dead tree, and I’ve been reminding myself to take pictures sometime. Well, I finally managed to do so and I established two things. 1) The autofocus on the camera I used sucks and 2) it’s not an eagle nest; it’s some sort of falcon with a white body. (The head is dark, even if it were an eagle it’d be a golden eagle, not a bald eagle.)

Postmodernism, a/k/a “Theory”

The other day I read a book review, regarding “Cynical Theories: How Activist Scholarship Made Everything about Race, Gender, and Why This Harms Everybody” by Helen Pluckrose and James Lindsay.

I must emphasize I have not read the book. According to the review, it doesn’t actually spend much time on many of the more politically noisome aspects of this latest version of “postmodernism,” but it is invaluable in going a step deeper in critiquing it than many others do.

A lot of the sheer nonsense pervading the Left is so crazy to anyone with a sane worldview that we find it hard to believe that the other side really believes this crap. But they do, because it is part and parcel of a nonsane worldview. And this broader worldview is discussed in the book. It makes Leftist nonsense seem at least somewhat sane within its own context.

We of course spend a lot of time here bashng “Critical Race Theory” (as it deserves) but other aspects of it are pernicious too and I thought I’d adapt the capsule summary of “Theory” I read in the review, here.

“Theory” apparently represents the latest wave of “postmodernism” which began in the 1960s with the work of Michel Foucalt. He argued that there is no such thing as objective truth. Or, if there is such a thing, it’s inaccessible to us because our knowledge is nothing but “narratives,” stories we tell each other and use to keep power.

Leaving aside the jokes playing off the fact that that statement itself is a claim to an objective truth, if there’s no such thing as objective truth, then basically anything goes.

Those two principles lie at the root of “Theory.” The next layer are four “attitudes” or methods.

1. the blurring of boundaries between intellectual and social categories. This can result in anything from men wearing dresses to scientists relying on anecdotes.
2. An emphasis on language as the tool that controls every aspect of life.
3. Cultural relativism–not just in morality (e.g., cultures where behaviors we consider corrupt are considered normal, for instance) but even in epistemology. In other words the methods we use for figuring out the world around us are only valid in our culture. Some other culture can adopt other rules for determining, say, if gravity works.
4. The lack of distinction between the individual and the universal. This means, among many other things, that “truths” (they insist on a plural there) have meaning only for a group. There aren’t any Steve truths, there are White Male truths. But there also isn’t a truth that is true for all of mankind either.

That’s the philosophic underpinning of today’s Left. No wonder they’ll believe such silly things.

It’s hard to predict what, exactly, the postmodernists will actually do with this, because as I said, these rules mean there are no rules for determining what is and isn’t true, much less what to do about a fact once it’s discovered. The PoMos themselves use bizarre jargon and revel in being incoherent. It’s a feature not a bug. And that’s a consequence of their basic beliefs. There’s no truth, “logic” is just one of many “ways of knowing” and one which must be tainted by racial/sexual/class bias…so what need to express oneself clearly or to give actual proof of one’s assertions?

Demanding that they be lucid is seen by them as a form of oppression; we’re trying to force them to use our standards.

Remember back in 1996 when Alan Sokal (a physicist) wrote a paper full of gibberish and it got accepted by a PoMo philosophy journal? The authors of this book repeated that in 2018, with over a dozen BS papers. One of those papers rephrased Mein Kampf in feminist jargon!

Cynical Theories makes the case that this stuff was apparently harmless up until the 1980s. The practitioners were unable to articulate an ideology, and couldn’t, therefore push to influence society. But in the 1990s they shifted gears. Keeping the two principles and four methods above, they fashioned a menu of separate specialist theories, e.g., “postcolonial,” “queer” and our current favorite, “critical race theory” among them, aimed at “deconstructing” things society used to take for granted, to show there was no objective truth there but just an attempt to hold power and oppress minorities. An example given in the review is “Disability and fat studies.” According to this even deaf or paralyzed people don’t suffer from their disabilities but rather from prejudice against them, held down by the network of power relations in society. So they argue that disabilities are yet another kind of “identity” and that trying to alleviate deafness or paralysis is actually oppressive and exploitative. And if a deaf or paralyzed person asks for help, he’s internalizing his own oppression.

Around about 2010 this garbage heap of “theories” coalesced into “Theory.” Collectivism is merged with the rejection of objectivity and now we have statements like “There’s no true truth but there are different truths for different categories of people.” Pluckrose and Lindsay explain “Having oppressed identities gives the oppressed a richer, more accurate view of reality-=hence we should listen to and believe their accounts of it.”

The dominant society, meaning, you guessed it, white male society, commits injustice against these groups when it fails to affirm their beliefs.

This is an inversion of Marxism, which claimed that the oppressed workers suffer from “false consciousness.” Now it’s the (alleged) oppressors who suffer from it, because they’ve been socialized to believe a certain set of “truths” that benefits them.

Special attention should be paid to the premise that language effectively constitutes reality, and blinds the majority to the fact that they are oppressing the minority. This accounts for one of the most aggravating aspects of the Left: They will insist on orthodoxy while simultaneously disowning their own efforts to enforce it.

And of course, this is why they conflate speech with violence. Because in their view, speech isn’t about reality, it is reality. A difference of opinion creates a power imbalance that threatens to erase a person’s only source of significance, which is other people “affirming” their “experience.” To listen, therefore, requires not just listening but actually affirming. Disagreement or criticism are inherently unjust.

There’s more, much more…I will probably be buying the book.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last week:

Gold $1844.90
Silver $27.53
Platinum $1232.00
Palladium $2949.00
Rhodium $27,600.00

This week, markets closed for the weekend at 3:00 PM Mountain Time

Gold $1880.70
Silver $27.63
Platinum $1172.00
Palladium $2834.00
Rhodium $25,500.00

Gold is doing very well. Platinum took a big hit, palladium fell 76 bucks on Friday alone, it’s now far away from its $3000+ dollar high point.. Rhodium is down, too, $1200 on Friday alone. Perhaps the PGM bubble is bursting? Realistically, it’s too early to tell.

Electricity and Magnetism (First Half)
(Part IV of a Long Series)

Introduction

The general outline of this story is to start off by putting you “in touch” with the state of physics at the beginning of 1895. Physicists were feeling pretty confident that they understood most everything. Sure there were a few loose ends, but they were just loose ends.

1895 marks the year when people began tugging at the loose ends and things unraveled a bit. In the next three years, three major discoveries made it plain there was still a lot to learn at the fundamental level.

Once I’m there I will concentrate on a very, very small object…that ties in with stars, arguably the biggest objects there are (galaxies are basically collections of stars). And we would never have seen this but for those discoveries in the 1890s.

It’s such a long story I decided to break it down into pieces, and this is the second of those pieces.

And here is the caveat: I will be explaining, at first, what the scientific consensus was in 1895. So much of what I have to say is out of date, and I know it…but going past it would be a spoiler. So I’d appreciate not being “corrected” in the comments when I say things like “mass is conserved.” I know that that isn’t considered true any more, but the point is in 1895 we didn’t know that. I will get there in due time. (On the other hand, if I do misrepresent the state of understanding as it was in 1895, I do want to know it.)

Also, to avoid getting bogged down in Spockian numbers specified to nine decimal places, I’m going to round a lot of things off. I used 9.8 kg m/s² last time for a number that’s actually closer to 9.80665, for instance, similarly for the number 32.

A couple of go-backs.

I’m actually used to dealing with newtons, joules, and watts as abbreviations, N, J and W. Of course now I’m writing for an audience of about six people many of whom haven’t taken the same classes I have, and often spelling the units out. Ignorantly, I’ve capitalized them because their abbreviations are capitalized. That was wrong. Although the names of the people the units are named after are, of course, capitalized, the units themselves should not be. I knew this 40 years ago, I forgot. For example, “The metric unit of power, the watt (W), was named after James Watt.”

I beg your pardon for this error.

More substantively, I thought I’d say a bit more about the dot product.

And this time, I will reference trigonometry. Just a teeny bit. This won’t hurt…much.

Pictorially, a dot product of two vectors is equal to the magnitude of the perpendicular projection of one vector onto the other, times the magnitude of that other vector.

OK, that’s a mouthful! Let’s call our two vectors A and B. Last time around we defined a symbol for the magnitude of a vector, so that the magnitude of A is ∥A∥ and the magnitude of B is ∥B∥. But let’s also make one more convention, let a_b be the magnitude of the projection of a onto b, and let b_a be the magnitude of the projection of b onto a.

So a dot product of A and B is equal to a_b∥B∥. But it works the other way, too, A•B = b_a∥A∥.

If you drop a line from the end of A to B, so that that line hits B perpendicularly, you’re said to have projected A onto B. In this case, the length of A‘s projection onto B is a_b=3.

But you can also project B onto A, as in the second part of the diagram. When you do that, the length of the projection, b_a is 2.4. I didn’t measure that, but I used ratios. The length of A is 5 (it’s part of a 3:4:5 right triangle), and the length of B is very obviously 4. The two triangles formed by the vectors and the dashed “dropped” line are similar, they share one angle where the two vectors meet, and a right angle, so all of the angles have to be the same. So if the hypotenuse of one is 5, while the other is 4, the other two sides must also both be cut by 20 percent. The projection of B onto A must therefore be 20% less in length than the projection of A onto B (which we know is 3), so that length must be 2.4.

In the left hand diagram, “the magnitude of the perpendicular projection of one vector [A] onto the other [B]” is 3. The “magnitude of that other vector [B]” is 4. The product is 12.

In the right hand diagram, these numbers are 2.4 and 5, respectively. The product of these two is also 12.

The dot product of these vectors is: [3, 4]•[4,0] = 3•4+4•0 = 12+0 = 12. So it works, at least in this example. I’ll let you look up the proof; I’ve only told you what it means.

What if both vectors are unit vectors? Since the vectors are of exactly the same length, their projections onto each other are the same, and since the vectors are of length one, the lengths of their projection onto each other will be one (if they are pointing in the same direction), or -1 (if they are pointing in opposite directions) or some number in between.

That number is the cosine of the angle between them, abbreviated cos.

The usual way of teaching trigonometry, shown in the first part of figure 2, involves drawing a “unit circle” (one with a radius of one), sticking this circle onto a Cartesian grid, and then drawing a line at some angle from the center of the circle to a point on the circle. Obviously the coordinates of that last point are going to differ depending on the angle, but the x value is the cosine, and the y value is the sine, abbreviated sin.

But you can look at the cosine of the angle as being the same thing as the projection of a unit vector onto a unit vector lying along the x axis.

Go back to my prior statement, about what a dot product was:

Pictorially, a dot product of two vectors is equal to the magnitude of the perpendicular projection of one vector onto the other, times the magnitude of that other vector.

With a pair of unit vectors being “dotted” together, both magnitudes in that sentence are 1. So, for unit vectors, it’s equivalent to

“a dot product of two unit vectors is equal to the magnitude of the perpendicular projection of one vector onto the other.”

But we just saw that the projection of one unit vector onto the other is the cosine of the angle between them. So if both vectors are unit vectors, the dot product of those vectors is the cosine of the angle between them.

If the first vector is not a unit vector, but is, say, twice as long then the magnitude of its projection onto the other is simply twice as long as well. In other words, that projection length is the magnitude of the vector, times the cosine of that angle.

You can go back to the original statement. The dot product of two vectors is the cosine of the angle between the vectors, times the magnitude of the first vector, times the magnitude of the second vector.

So the formal definition of a dot product is:

A•B = ∥A∥∥B∥cosθ

where θ is the angle between the two vectors.

This gives you a sneaky way to figure out the angle between two vectors. Take their dot product. Then divide by the magnitude of the first vector, and divide again by the magnitude of the second vector. You now have the cosine of the angle between them. You can look up the “inverse cosine” (i.e., the reverse of taking the cosine). Today, you can use a calculator (or calculator app). A few decades ago, a fancy slide rule might have a scale on it for cosines, from there you can look up the angle. Also you could look it up in a table. Sines and cosines are actually very well known functions.

There are a number of angles with well-known cosines that are actually expressable as somewhat-sane numbers. 45 degrees, for instance, is an angle at which the sine and cosine are equal, (see part B of figure 2). You can draw a right isosceles triangle there, which means the two legs are equal. Using Pythagoras, c² = b² + a² for right triangles (with c being the side opposite of the right angle), and knowing that c = 1, and a = b, 1 = 2a². So a² = 1/2. Now a is equal to the cosine, or the sine in this case, so both are equal to the square root of 1/2, sqrt(1/2) (sorry, I can’t do fancy square root signs here). That’s 1/sqrt(2), but mathematicians hate it when you put a radical in the denominator, so they multiply top and bottom by sqrt(2) and get sqrt(2)/2. This is roughly 0.707. Similar reasoning will get you the sines and cosines of 135, 225, and 315 degrees, you’ll have to put negative signs in as appropriate.

60 and 30 degrees are other convenient angles. For instance with 60, you can get the answer from realizing that you can draw an equilateral triangle here, as shown in part 3. The X line, the slanted line, and a third line are all length one, and that’s a 60 degree angle there. It’s a symmetrical triangle, so the cosine has to be 1/2. The sine can be had from Pythagoras, too: sqrt( 1 – (1/2)²) = sqrt( 3/4 ) = sqrt(3)/2. Sqrt(3) = 1.732 (remember, Washington’s birth year), sqrt(3)/2 = roughly 0.866.

You can use similar reasoning for 30, 120, 150, 210, 240, 300, and 330 degrees.

Thes are all “magic angles” (as I called them last week) because you just know the sine and cosine and in some cases it’s even a nice nifty fraction like 1/2.

Most angles in whole degrees give you absolutely ugly sines and cosines.

OK, with that exceedingly gentle intro to trigonometry and the additional info on dot products out of the way…

Electricity

It has been known since at least 600 BC that amber (fossilized tree sap), when rubbed, could attract light objects. This was noted by Thales of Miletus. (There is no extant record on whether Thales had difficulty with the sheets coming out of his clothes dryer.)

Sometime in the next 2000 years, someone noticed that glass exhibited the same behavior.

In 1723 Charles Francois Du Fay, a French physicist, realized that actually, glass and amber didn’t quite behave exactly the same way. Whatever it was they were doing was different in a rather interesting way.

Suspend two corks on silk threads. Buff up a piece of amber, touch one of the silk threads. The two corks are attracted to each other, somewhat. Buff up the piece of amber again, and touch the other silk thread. Now the corks actually repel each other, somewhat more strongly.

Whatever it is that’s in the amber that makes it attract small objects, when introduced to two different objects, caused them to repel each other, as if the whatever-it-is repels itself.

Repeat this experiment, but this time touch the second thread with a rubbed bit of glass. Now the two corks attract strongly. And if you repeat again, and touch both threads with the bit of rubbed glass, the corks repel each other again.

There is, in other word a resinous electricity (from amber) and a vitreous electricity, from glass, and they appear to be two different things, but able to interact with each other.

So vitreous electricity repels itself, but attracts resinous electricity (and vice versa), and resinous electricity repels itself too. They both seem to attract small things that don’t have any electricity in them at all. Like repels like and attracts the other.

At this point Du Fay came up with a fluid theory of electricity. Each kind of electricity was a different sort of fluid that would flow from solid object to solid object.

In the 1740s an otherwise obscure individual by the name of Benjamin Franklin in Pennsylvania did some more work. He was able to show that if you took an object with one of the two kinds of charge, and touched it with an object of the other kind, the charges disappeared, as if they had cancelled each other out.

Franklin came up with the single fluid theory. In this one electricity was a sort of fluid and under ordinary circumstances, an object would have a certain normal amount of it. But when it was in surplus, you saw one kind of charge, when it was in deficit, you saw the other kind. (In very similar fashion, surplus money can be used to pay off debt, a negative amount of money.)

And indeed this analogy suggests that the charge with the surplus of fluid could be considered positive, and the charge from a deficit of fluid could be called negative. This would be mathematically convenient. It wasn’t meant in any sort of pejorative way.

That is precisely what Franklin chose to do. However, he had no idea which kind was the surplus! He labeled the vitreous charge “positive” and the resinous charge “negative” and it has been this way ever since. His chances of getting it right (assuming a fluid was moving) were 50-50.

The charges could just as easily have been labeled black and white or red and green or yin and yang. But by Franklin’s time mathematical rigor had begun to pervade science, and so positive and negative, they were.

One difficulty with Franklin’s theory was that although one could imagine a fluid repelling itself (like two positive charges would do), but it was more difficult to imagine the lack of such a fluid in two objects creating a repelling force. Nonetheless, Franklin’s formulation was a lot more widely accepted than Du Fey’s.

One can also have different strengths of charges; one piece of rubbed glass might have twice as strong a charge as another. That, presumably, meant the first had twice as much of the fluid in it as did the second. Similarly, pieces of amber could have different deficits of the fluid. In order for charges to completely cancel out, it turns out, they must have equal magnitude but be opposite. If one is of greater magnitude than the other, then the result of the cancellation will be a slight amount of that charge, the leftover part that couldn’t be cancelled out by the other.

Imagine coming up with some way to measure charge, and you have a positive 3000 charge and another negative 2800 charge. Putting the two together, you’re left with a positive 200 electric charge, just like you’d get from adding the numbers +3000 and -2800.

There is in fact a unit of electric charge, the coulomb, named after Charles A. de Coulomb, and it seems to be a very large unit.

Who was Coulomb? He formulated the law of force between electric charges. This law superficially resembles Newton’s law of gravity. F₁₂ is the force exerted by charge 1 on charge 2.

F₁₂ = (kq₁q₂ / r²)•ȓ₁₂.

As a reminder Newton’s law of gravity was

F₁₂ = -(Gm₁m₂/r²)•ȓ₁₂.

So instead of the masses, we have q, the electric charge of the objects, and we have a different constant, k. G was a small number, 6.67 x 10^-11, indicating that two one kilogram masses a meter apart would attract each other with a force of 6 trillionths of a Newton.

The k in Coulomb’s law is 8.99 x 10⁹. In other words, nine billion.

So two one Colomb charges a meter apart act upon each other with a force of nine billion Newtons. Which is almost the weight of a billion kilograms on earth, or about a million English-system tons. From one Coulomb acting on another.

As I said a Coulomb is a huge unit! The sheets in your dryer don’t stick to each other quite that hard, but when you remember static electricity can lift small objects against gravity, it’s pretty plain the electric force is likely inherently stronger than gravity.

Although Coulomb’s Law and Newton’s law of universal gravitation look a lot alike, with charge and mass filling in for each other, and different fudge factors, there’s one very important difference.

Newton’s law has a minus sign in it. Coulomb’s law does not. The minus sign serves to make gravity an attractive force, because it makes the force vector point the opposite way as the displacement unit vector. This doesn’t happen with electric charges.

But don’t we have situations where electric charges attract? Sure we do. And even though this formula describes a repulsive force, it does allow for this, because the result is negative when some part of the formula is negative; r² must be positive, k is positive, so the only way that can be is if q₁q₂ is negative. If both charges are positive, the product is positive…and they will repel. If one is positive and the other negative, the product is negative, and it’s like gravity; they attract. Finally if both charges are negative the product is positive, and the two charges again repel each other.

So that’s how charges behave. It’s oddly like gravity and also oddly unlike gravity. And it’s a lot stronger than gravity.

Conservation of Electric Charge

It eventually became evident that electric charge is conserved. If your system starts out with 0 total, in other words, “electrically neutral,” you can create a charge somewhere in it, but always at the cost of creating an opposite charge somewhere else in the system–again, as if some amount of fluid had moved from one place to another. And if there is a charge somewhere in the system, it can only disappear if it’s combined with the opposite charge from somewhere else in the system.

What of the small objects…dog fur, scraps of paper, and so on, that are attracted to an electric charge, even though they’re neutral? For example, imagine dog hair stuck to positively charged glass.

We know the dog hair is not simply charged the other way. negatively, because it’s attracted to both kinds of charge.

As it turns out the electric fluid in the dog hair–it has some in it, just exactly enough to be neutral–is repelled by the glass’s positive charge, and ends up at the far end of the hair. Of course, this means the end of the hair closest to the glass now has a negative charge. And the negatively charged end is closer to the glass than the positively charged end is, so the attractive force is stronger than the repulsive force. Voila! The (overall) neutral object now sticks to the positive charge. Even if the hair is lying flat against the glass (and it probably is), the side touching the glass is closer than the side far away.

For the most part, the phenomena we’ve been talking about involves static electricity, electricity that is not moving. Sure, one of our experiments involved having it move along a silk thread. And there were also Leyden jars which could hold a substantial charge and would release it when the contacts were touched—sometimes enough charge to knock a man down. But for the most part, the charges didn’t move.

But electricity is much, much MUCH more interesting when it is moving, especially either steadily or in an oscillating fashion! More on that later; I have to set this aside and start another “thread” of thought now.

Magnetism

Another phenomenon, very similar to electricity in some ways and rather different in others, also turned up in ancient times. There were occasional rocks that would attract iron. They would also attract each other. But sometimes they repelled each other. And it turned out that the SAME rock would have a part that would repel the other rock, and one that would attract it. On the other hand, this didn’t matter when the rock was interacting with iron; either end would attract it.

This, of course, is what we now know as magnetism. And those two ends that attract or repel each other became known as poles.

That’s because a magnet, left free to swivel, will always point one of its two poles roughly toward the Earth’s north pole, that’s called the north pole of the magnet. The other is the south pole of the magnet. When it becomes a matter of representing these things mathematically, the north pole is considered “positive.”

Very much like electricity, similar poles repel, opposite poles attract. (Ironically, this means the Earth must be a giant magnet, with that magnet’s south pole near the north (geographic) pole, so it can attract magnets’ north poles.)

What happens if you break a magnet in half to try to separate the north pole from the south pole? You get two smaller, weaker magnets, each with north and south poles. The broken end of the north side of the old magnet is now a south pole, and the other side of the break is now the north pole of the other new magnet.

In fact, no matter how small you break a magnet, you will never succeed in having just one pole. This sort of thing, if it existed, would be called a “magnetic monopole” and it’s a true unicorn.

Magnets, too attract or repel each other in inverse propotion to the square of how far apart they are–which is mathematician speech for “there’s an r² in the denominator.” This is hard to see or even use, though, because there’s always an opposite pole nearby which partially cancels things out.

Magnetic poles didn’t seem to move around within objects like electric charge does. But there was a sort of conservation law; in breaking a magnet in two, you still had equal numbers of north and south poles And the fact that there are no monopoles tells you that the total amount of “north pole” must be equal to the total amount of “south pole” because they always come in pairs.

Magnets, too, can be much more interesting when they’re moving.

Electricity Moving. Work and Potential

If there is a force, then work can be done.

Imagine an object, a kilogram in mass, with a coulomb of positive charge on it. Allow it the freedom to move. Put a fixed charge nearby, on an object that cannot move.

If you space things properly, that charged object will start to accelerate, at 1 meter per second per second. As if one newton of force were being applied to it.

That’s because there is a newton of force being applied to it, a newton of electrical force, not gravitational force, and not a solid thwack administered by an experimenter. And after a meter of this, the electrical force has done one joule of work, just like with every other kind of force.

In fact, you can draw an analogy here between the sort of potential we talked about, where the height of a cliff was related to how much work gravity would do on an object dropped off of it, to what the electrical force does to a charged object.

If, going from point A to point B, a coulomb charge has a joule of work done to it, the electrical (not gravitational) potential between A and B is one volt. Yes, that volt. Named after Allesandro Volta, about whom, more in a bit, and abbreviated with a capital V.

So the equation here is work = potential x charge. Double the potential, double the work; double the charge, double the work. Or 1J = 1V x 1C.

Equivalently 1V = 1J/C.

And similar to gravitational potential where twice as much work gets done by doubling the mass, you can get twice as much work out of a one volt potential, by having it operate on two coulombs.

Didn’t we just see that a coulomb is a gigantic charge? Or at least, that it exerts a very strong force, so big that no doubt we’ve never seen a coulomb out in the real world? What dang use is a volt? It must be pretty tiny to get only one joule out of a coulomb!

The fact of the matter is, though, that when electricity moves, a coulomb isn’t all that much, particularly if you can get it to move for a prolonged period of time.

This was quite a bit different from the static electricity games that people had been playing up to now. Sure, you could occasionally get static electricity to move (if not careful, it would move through you), but it would usually just do it all at once, and once it had moved there were no positive or negative charges. It was moving from a high voltage to a low voltage, all at once. Sort of like dropping a rock (hopefully not on your foot). Once the rock is at the bottom, you’re done getting work out of the system, and you’re done quite quickly.

Imagine, though, turning on a faucet and getting a continual stream of mass to fall. (Or imagine a waterfall.)

We figured out how to do this in the very late 1700s. The story starts with an Italian named Galvani in the late 1700s; he was dissecting frogs and noticed that a spark could make the leg muscles twitch, even though the frog was quite thoroughly dead. Then he noticed that if he touched it with two different metals, he could also make it twitch.

That was the clue that Allesandro Volta (1745-1827) needed. In 1799 he created something we now call a “voltaic pile.” Start with a disk of copper. Place on top of it a disk of cardboard soaked in salt water. Place on top of that a disk of zinc.

Run a metal wire from the copper plate to the zinc plate, and electricity will flow through it from the copper to the zinc. There’s clearly a “push” being given to the electrical fluid in the wire. That push is a potential of about 3/4 of a volt, but Allesandro Volta certainly didn’t call it that.

If you stack these, you can build up higher and higher voltages. Place another copper disk directly on the zinc one, another bit of salt-water-cardboard, another zinc disk, and the total is 1.5 volts. Do it again, and now you have 2.25 volts. And so on. As long as you put negative zinc right next to positive copper in your stack of these sandwiches, you build up voltage.

But the big thing is, electricity could now be generated chemically, and not just rubbing things together, and it was sustained for some period of time until this pile, what we now call a battery, ran down.

In just a few years, ending in 1808, Sir Humphry Davy was able to reverse things; instead of chemistry making electricity, he got electricity to do chemistry. He was able to isolate no less than seven elements from compounds that had previously proven to be too tightly bound to be broken by conventional chemical means. Up til then we were reasonably confident those elements were there; we just couldn’t actually prove it beyond a shadow of a doubt by getting those elements out of their compounds.

And as early as 1800 electricity from a voltaic pile was used to break down water into hydrogen and oxygen.

The thicker the wire, the faster the battery would run down. Almost as if more electrical fluid could “fit” in a thicker wire.

And now we have hit the concept of electric current. How much electricity is moving? That’s how much electric current there is.

One ampere is one coulomb flowing past a point, every second. It was named after Andre Marie Ampere (1775-1836). He did a lot of the early work on what he called “electrodynamics.”

If you look in your breaker box, you’ll likely see a lot of switches labeled 12, 15, 20 or even more “A”. That’s amperes, and when one of those breakers flips, you’ve drawn more than that many amperes through that switch. In a circuit whose breaker is labeled 12, twelve coulombs will pass through that breaker every second.

With all those coulombs moving around why hasn’t your house blown apart (or been sucked into a vortex) from all those coulombs attracting or repelling each other?

Because the electrical fluid moves, and it doesn’t accumulate anywhere. A coulomb flows from one side of the breaker to the other, but another coulomb of fluid is right behind it, so there’s no deficit to create a resinous/negative charge. And the fluid downstream from your breaker also moved on, leaving space for the coulomb that just flowed through the breaker. No accumulation, no net positive charge (and no places low on fluid to have a negative charge).

The wire forms a closed loop, with your house at one end, and a power source on the other, something that creates an electrical potential, so that current will flow from high to low. (This is sometimes called Electromotive Force, or EMF, and abbreviated with a script capital E: ℰ.)

In a battery the current is “pushed” by the battery through the wire, through whatever it is you’re using the electricity to operate, and back along another wire to the battery…which uses chemical energy to do work, and give it another push around the loop. So a battery converts chemical energy to electrical energy. Once it runs out of chemicals it can react, it’s dead. (This is another aspect of the conservation of energy.)

One difference between a battery and your house wiring is that in your house wiring the current switches direction, back and forth, sixty times a second (50 in Europe and some other parts of the world). This is called “alternating current.” A battery doesn’t switch back and forth, and it’s called “direct current.”

Digression

OK, I’m going to shift for a moment from physics to the metric system itself.

The newton, joule and watt are called “derived units.” They come from combinations of other, more fundamental units, the meter, the kilogram, and the second. Length, mass, and duration are very different things from each other, but force, for instance, has to do with mass, length and duration. But when it comes to electricity, we have yet another thing that’s different from everything else. So something having to do with electricity should be a fundamental unit. The metric system has seven fundamental units; we’ll probably only touch only two of the remaining three.

You would think that the fundamental unit for electrical things would be electric charge, but you’d actually be wrong. The “fundamental unit” having to do with electricity in the metric system is the ampere. The coulomb is defined as one ampere, flowing for one second (C = A•s); the volt is then defined as I stated above.

But it’s even a bit crazier than that. There are two metric systems! The one I’ve used all along is MKS, for “meter kilogram second” because that’s what it derives other units from. But there is an older, mostly disused system called “CGS” for “centimeter gram second,” it derives its unit of force, and energy and so on from centimeters, grams and seconds. Its unit of force is called the dyne—1 g cm/s². When you consider that the gram is 1/1000th of a kilogram, and a centimeter is 1/100th of a meter, it should be no surprise that the dyne is 1/100,000 of a newton. The unit of energy is called the erg, and it is 1/10,000,000 of a joule. These are tiny, tiny units. The MKS units are easily “felt” by people: who hasn’t lifted 100 grams (weighing about one newton) about a meter and done a joule of work? But that’s ten million ergs!

Returning to Electricity…

OK, back to the main story.

Returning to our electrical circuit, from battery positive terminal through something that uses the electricity for energy, then back to the negative terminal of the battery, current is flowing.

What if there is a break in the wire? Won’t the electricity simply pile up?

Only the slightest, tiny bit. As more electrical fluid goes down the wire an unbalanced positive charge builds up, it begins to repel the fluid headed its way and forces it to a stop. This happens very quickly, effectlively, the current just comes to a screeching halt the instant the break happens. And if you measure the potential across both ends of the break, it’s now equal to the potential of the battery, whereas before the break, there was no potential difference at that point, but current was flowing through it.

Electricity is very eager to move, at least in good conductors; it really hates piling up, because a pile of it is a bunch of the same charge confined to a small space, and every bit of that repels every other bit, and hard.

Is there any constraint on how much current flows? Certainly. Every material, even a wire, has a resistivity to the flow of electricity. The more resistance, the less current will flow for the same voltage. On the other hand, if you double the voltage, that’s double the push, and twice as much current will flow through that same object. This works pretty consistently (until you reach the absolute carrying “ampacity” of the stuff and it heats up and melts or vaporizes, at which point, you’re done with that bit). Given a volt put across two opposite sides of a cube of the stuff, how much current will flow? Given that number, you can figure out how much resistance a certain object will have. It increases with length, and decreases with cross-section, so you can figure out the resistance of a wire, or any other object you want to carry a current, if you know the resistivity of the stuff it’s made of.

If the object the current is trying to flow through allows one amp through when it’s subjected to a volt, it has a resistance of one ohm, named after Georg Simon Ohm, who figured out that current flow was proportional to the applied voltage, and the proportion was different for every kind of material. In fact, it’s a law: the current through an object is equal to the voltage across the object, divided by the resistance.

I = E/R

I is current, don’t ask me why. E is from “Electromotive Force” and R is…wait for it…the resistance. Or to put it in metric units,

1 A = 1V/Ω

That funky symbol at the end is a capital Greek letter omega (as in “alpha and omega”), and perhaps it was selected to be the symbol for the derived unit ohm, as a sort of pun (ohm-ega).

If you have a circuit, from the positive end of a battery through three different resistances and back to the battery, you can measure the voltage across those three items and they will all have a pro-rata share of the voltage the battery is supplying. Say, for instance, it’s a 12V battery, and you have three lights hooked up to it, each light is 100 ohms. They’re all equal, and so the voltage across each light will be 4V.

The current through any one of these lights will be 4V/100 ohms, or 0.04A. The same current goes first through one light, then the second, then the last, so it’s a good thing all of those currents are the same (or current would be coming in from nowhere).

By the way, on diagrams like this, for educational purposes, the wires are assumed to have zero resistance. So the voltage drop from the battery to the top terminal of the bulbs is E=IR = 0.4A • 0Ω = 0V. Likewise the wire between the bulbs has zero voltage drop.

Stringing a load end to end like that is known as wiring in series and usually is a stupid way to do things. (If one bulb blows out the circuit is broken and none of them work. Also, adding more bulbs increases the total resistance, reducing the current, and the total amount of light is actually less.)

Connect each of the three bulbs directly to the battery at both ends. This is parallel, because it splits the current into three separate streams. Each bulb now has 12 V across it, not 4, and the current through each bulb is 0.12A. Since each bulb gets a separate stream of current, the currents add up (instead of the voltages) and the battery is delivering 0.36A. Adding more bulbs adds more light, they each continue to use the same current as before.

When wiring up a house, if there are, say, multiple lights controlled by one circuit, your electrician wired them in parallel, not in series. (Or he has made a rookie mistake.)

OK, one more thing, before we alas, must call it quits…prematurely.

Imagine a 1A current flowing. That’s one colomb/second (1 C/s). Imagine it’s flowing because of one volt of potential. A volt is 1 J/C.

What happens when you multiply current by potential?

C/s • J/C.

The coulombs cancel, and you’re left with J/s. Which is power, in watts. The same watts we had when we were playing with weights and forces.

(Incidentally, in the US, we tend to think of electrical things in watts–light bulbs especially. But with mechanical things, even an electric circular saw, we think of their power in horsepower. It’d be really odd for someone to brag about how many watts his car engine puts out, though he could. On the other hand, it’s perfectly normal in Europe though even they have a residual use of horsepower, judging at least from car marketing materials (though maybe that’s for the benefit of us Yanks). But just so you have a feel for the difference, one horsepower is 746 watts.)

But this shouldn’t be any surprise. Remember that a volt is what you needed to get a coulomb to do a joule’s worth of work. A current of 1 ampere means that a coulomb of electricity is having this done to it every second, in other words a joule of work is being done every second…which is a watt.

So P (for power) = I (for current…again, don’t ask me why) x E (for voltage).

We can now write many different equivalencies for the watt:

1W = 1J/s = 1V•A = 1 kg•m²/s² = 1 V•C/s…

So we’ve figured out that electricity has potential, it has current, it has resistance and it has power, many of these analogous to gravity, many not really all that analogous at all.

Going back to those two diagrams above, the first has 0.04A flowing through a 12 V potential drop, that’s 0.48 W. The second has 0.36A flowing through a 12 V potential drop, for 4.32W. The latter circuit delivers nine times as much power as the former. Batteries are rated in A•h, not watt-hours, so what matters is how much current it delivers. Because it’s delivering nine times as much current (as well as nine times the power), that battery will die nine times faster.

Now going back to house breaker panels, we know the voltage (on average) is 120V. The breaker says it’s a 20A breaker. Multiply the two together, and the breaker carries 2,400 watts. Why not just label the breaker that way?

Because a breaker is designed to protect the circuit which has a limit on how much current it can carry. The circuit’s capacity is unaffected by the voltage of delivery but it had better not draw more than 20A. In fact the same breaker could conceivably be used in Europe, where the supply voltage is 220V, and therefore be able to pass 220V x 20A = 4,400 watts. (I don’t know if it’s physically compatible with the way their systems are laid out, though, so don’t go selling unused breakers to people in Europe to raise money when the Great Fiscal Apocalypse finally hits.)

There is much, much more to this story, we’re still in the early 1800s. I am sure Wolf will tell you I am quitting before the interesting part. And I am!

But I don’t want this to get overlong, and I still have to draw the diagrams, and it’s already 9PM in Wolf’s time zone.

I’m going to cover a totally different topic next week, then bounce back to this story the week after.

There is a mystery here, you might already see it, but it’s still a mystery in 1895, so let’s save it until we get there.

And Joe Biden didn’t win.

To Be Continued…

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

This Sanctuary Sunday Open Thread, with full respect to those who worship God on the Sabbath, is a place to reaffirm our worship of our Creator, our Father, our King Eternal.

It is also a place to read, post and discuss news that is worth knowing and sharing. Please post links to any news stories that you use as sources or quote from.

In the QTree, we’re a friendly and civil lot. We encourage free speech and the open exchange and civil discussion of different ideas. Topics aren’t constrained, and sound logic is highly encouraged, all built on a solid foundation of truth and established facts.

We have a policy of mutual respect, shown by civility. Civility encourages discussions, promotes objectivity and rational thought in discourse, and camaraderie in the participants – characteristics we strive toward in our Q Tree community.

Please show respect and consideration for our fellow QTreepers. Before hitting the “post” button, please proofread your post and make sure you’re addressing the issue only, and not trying to confront the poster. Keep to the topic – avoid “you” and “your”. Here in The Q Tree, personal attacks, name calling, ridicule, insults, baiting and other conduct for which a penalty flag would be thrown are VERBOTEN.

In The Q Tree, we’re compatriots, sitting around the campfire, roasting hot dogs, making s’mores and discussing, agreeing, and disagreeing about whatever interests us. This board will remain a home for those who seek respectful conversations.

Please also consider the Guidelines for posting and discussion printed here: https://www.theqtree.com/2019/01/01/dear-maga-open-topic-20190101/

How Big Is Your God?

Yours, O Lord, is the greatness and the power and the glory and the victory and the majesty, indeed everything that is in the heavens and the earth; Yours is the dominion, O Lord, and You exalt Yourself as head over all. (1 Chronicles 29:11)

Robert D. Wilson (1856-1930) was a Presbyterian scholar who devoted his life to showing the Hebrew Bible’s reliability. In proving the accuracy of the Old Testament manuscripts, Wilson learned 45 languages, including all languages into which the Scriptures had been translated up to 600 AD. He was a Professor at Princeton Seminary and Westminster Seminary.

Wilson went to hear one of his students (Donald Barnhouse) preach and said, “I came to see if you are a Big-Godder or a little-godder, then I know how your life and ministry will unfold.” Wilson explained that people with a little god are always in trouble. Their god can’t create or do miracles. He can’t forgive big sins or help people change their lives in big ways. Their little god can’t take care of the Scriptures’ inspiration and transmission to us. He doesn’t intervene for His people or answer prayer. These people have a little god who is really no god at all.

Others have the great, awesome, almighty, invincible God—the Lord of the Bible—Father, Son, and Holy Spirit. This God speaks and it is done; He commands and it stands firm; He shows Himself strong on behalf of those who love, fear, trust, and obey Him. Dr. Wilson said, “You, young man are a Big-Godder, and the Lord will bless your life and ministry. He will use you for His praise.”

Christ can save, He can cleanse, He can keep, and He will. Christ can do anything but fail. He’s the Alpha and Omega, the beginning and the end. He’s the fairest of ten thousand to my soul. God can do anything, anything, anything. God can do anything but fail.

Near age 70, Wilson finished a lecture on the trustworthiness of Scripture and said to his students, tears streaming down his face: “There are many mysteries in life I can’t understand, many things hard to explain. But I can tell you with absolute assurance: Jesus loves me, this I know, for the Bible tells me so!”

God said, “I will cause all my goodness to pass in front of you, and I will proclaim my name, the Lord, in your presence. I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.” …And He passed in front of Moses, proclaiming, “The Lord, the Lord, the compassionate and gracious God, slow to anger, abounding in love and faithfulness, maintaining love to thousands, and forgiving wickedness, rebellion and sin….” (Exodus 33:19; 34:6-7)

How big is your God? How much is He in control? Does He have the whole world and you in His hands? Is He big enough to win against sin, Satan, death, disease, and all false religions?

Do you not know? Have you not heard? The LORD is the everlasting God, the Creator of the ends of the earth. He will not grow tired or weary, and His understanding no one can fathom. He gives strength to the weary and increases the power of the weak. Even youths grow tired and weary, and young men stumble and fall; but those who hope in the LORD will renew their strength. They will soar on wings like eagles; they will run and not grow weary, they will walk and not be faint. (Isaiah 40:28-31)

* https://wohbm.org/are-you-a-big-godder/

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Well, then, if God is a Big God . . .

Why is it that bad things happen to good people?

We live in a world of pain and suffering. There is no one who is not affected by the harsh realities of life, and the question “why do bad things happen to good people?” is one of the most difficult questions in all of theology. God is sovereign, so all that happens must have at least been allowed by Him, if not directly caused by Him. At the outset, we must acknowledge that human beings, who are not eternal, infinite, or omniscient, cannot expect to fully understand God’s purposes and ways.

The book of Job deals with the issue of why God allows bad things to happen to good people. Job was a righteous man (Job 1:1), yet he suffered in ways that are almost beyond belief. God allowed Satan to do everything he wanted to Job except kill him, and Satan did his worst. What was Job’s reaction? “Though he slay me, yet will I hope in him” (Job 13:15). “The LORD gave and the LORD has taken away; may the name of the LORD be praised” (Job 1:21). Job did not understand why God had allowed the things He did, but he knew God was good and therefore continued to trust in Him. Ultimately, that should be our reaction as well.

Why do bad things happen to good people? As hard as it is to acknowledge, we must remember that there are no “good” people, in the absolute sense of the word. All of us are tainted by and infected with sin (Ecclesiastes 7:20; Romans 3:23; 1 John 1:8). As Jesus said, “No one is good—except God alone” (Luke 18:19). All of us feel the effects of sin in one way or another. Sometimes it’s our own personal sin; other times, it’s the sins of others. We live in a fallen world, and we experience the effects of the fall. One of those effects is injustice and seemingly senseless suffering.

When wondering why God would allow bad things to happen to good people, it’s also good to consider these four things about the bad things that happen:

1) Bad things may happen to good people in this world, but this world is not the end. Christians have an eternal perspective: “We do not lose heart. Though outwardly we are wasting away, yet inwardly we are being renewed day by day. For our light and momentary troubles are achieving for us an eternal glory that far outweighs them all. So we fix our eyes not on what is seen, but on what is unseen, since what is seen is temporary, but what is unseen is eternal” (2 Corinthians 4:16–18). We will have a reward some day, and it will be glorious.

2) Bad things happen to good people, but God uses those bad things for an ultimate, lasting good. “We know that in all things God works for the good of those who love him, who have been called according to his purpose” (Romans 8:28). When Joseph, innocent of wrongdoing, finally came through his horrific sufferings, he was able to see God’s good plan in it all (see Genesis 50:19–21).

3) Bad things happen to good people, but those bad things equip believers for deeper ministry. “Praise be to . . . the Father of compassion and the God of all comfort, who comforts us in all our troubles, so that we can comfort those in any trouble with the comfort we ourselves receive from God. For just as we share abundantly in the sufferings of Christ, so also our comfort abounds through Christ” (2 Corinthians 1:3–5). Those with battle scars can better help those going through the battles.

4) Bad things happen to good people, and the worst things happened to the best Person. Jesus was the only truly Righteous One, yet He suffered more than we can imagine. We follow in His footsteps: “If you suffer for doing good and you endure it, this is commendable before God. To this you were called, because Christ suffered for you, leaving you an example, that you should follow in his steps. ‘He committed no sin, and no deceit was found in his mouth.’ When they hurled their insults at him, he did not retaliate; when he suffered, he made no threats. Instead, he entrusted himself to him who judges justly” (1 Peter 2:20–23). Jesus is no stranger to our pain.

Romans 5:8 declares, “But God demonstrates his own love for us in this: While we were still sinners, Christ died for us.” Despite the sinful nature of the people of this world, God still loves us. Jesus loved us enough to die to take the penalty for our sins (Romans 6:23). If we receive Jesus Christ as Savior (John 3:16; Romans 10:9), we will be forgiven and promised an eternal home in heaven (Romans 8:1).

God allows things to happen for a reason. Whether or not we understand His reasons, we must remember that God is good, just, loving, and merciful (Psalm 135:3). Often, bad things happen to us that we simply cannot understand. Instead of doubting God’s goodness, our reaction should be to trust Him. “Trust in the LORD with all your heart and lean not on your own understanding; in all your ways acknowledge Him, and He will make your paths straight” (Proverbs 3:5–6). We walk by faith, not by sight.

* https://www.gotquestions.org/bad-things-good-people.html

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On this day and every day –

God is in Control
. . . and His Grace is Sufficient, so . . .
Keep Looking Up

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“This day is holy to the Lord your God;
do not mourn nor weep.” . . .
“Go your way, eat the fat, drink the sweet,
and send portions to those for whom nothing is prepared;
for this day is holy to our Lord.
Do not sorrow,
for the joy of the Lord is your strength.”

If you keep your feet from breaking the Sabbath and from doing as you please on my holy day, if you call the Sabbath a delight and the Lord’s holy day honorable, and if you honor it by not going your own way and not doing as you please or speaking idle words, then you will find your joy in the Lord, and I will cause you to ride in triumph on the heights of the land and to feast on the inheritance of your father Jacob. For the mouth of the Lord has spoken. Isaiah 58:13-14

Another week, another deluge of BS from the White House and from the Controlled Opposition. Not much has really happened, so with that noted, on we go.

On the plus side it looks like the Covid mask is slipping. A lot of places here are now saying no mask if you’ve been “vaccinated.” (And that’s based on the CDC, the governor has not dropped the mask mandate.) The COVIDschina goes on.

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot Prices

Gold $1831.70
Silver $27.54
Platinum $1257.00
Palladium $2980.00
Rhodium $27,400.00

This week, 3 PM MT on Friday, markets closed for the weekend

Gold $1844.90
Silver $27.53
Platinum $1232.00
Palladium $2949.00
Rhodium $27,600.00

Gold has broken out, but seems content to stay at this new higher level. Silver has not gone much of anywhere, down one cent. Platinum down (and it had to climb to close at this level today!). Palladium didn’t stay above 3000 for long, but perhaps it will punch through decisively soon, it too was climbing today.

Energy and Potential
(Part III of a Long Series)

Introduction

The general outline of this story is to start off by putting you “in touch” with the state of physics at the beginning of 1895. Physicists were feeling pretty confident that they understood most everything. Sure there were a few loose ends, but they were just loose ends.

1895 marks the year when people began tugging at the loose ends and things unraveled a bit. In the next three years, three major discoveries made it plain there was still a lot to learn at the fundamental level.

Once I’m there I will concentrate on a very, very small object…that ties in with stars, arguably the biggest objects there are (galaxies are basically collections of stars). And we would never have seen this but for those discoveries in the 1890s.

It’s such a long story I decided to break it down into pieces, and this is the second of those pieces.

And here is the caveat: I will be explaining, at first, what the scientific consensus was in 1895. So much of what I have to say is out of date, and I know it…but going past it would be a spoiler. So I’d appreciate not being “corrected” in the comments when I say things like “mass is conserved.” I know that that isn’t considered true any more, but the point is in 1895 we didn’t know that. I will get there in due time. (On the other hand, if I do misrepresent the state of understanding as it was in 1895, I do want to know it.)

Also, to avoid getting bogged down in Spockian numbers specified to nine decimal places, I’m going to round a lot of things off. I used 9.8 kg m/s² last time for a number that’s actually closer to 9.80665, for instance, similarly for the number 32.

Revisiting Gravity with Vectors.

We now know something about vectors, and in light of that, we can go back a ways now to gravitation and take a look at it again.

The law of gravitation we discussed looked like this:

F = Gm₁m₂/r²

But force is actually a vector because it has a direction. This formula is full of nothing but scalars, so it only tells you the magnitude or size of the force vector, not its direction.

If you have a magnitude without a vector, then if you use it to scalar-multiply ia vector of length exactly one, you now have a vector of the right magnitude, because scalar multiplication changes the magnitude of the vector. And if that one-length vector pointed in the right direction, the new vector does too, because multiplying a vector by a scalar does not change its direction.

A vector of length 1 is called a “unit vector” and is a very useful part of the toolkit.

Sometimes it’s necessary to take a vector that isn’t a unit vector and determine the unit vector that matches it.

As you might have guessed, the way to do that is to take your vector, call it V, determine its magnitude, and divide it by the magnitude of V, which is to say, to multiply it by 1-divided-by-the-magnitude. (If multiplication is defined, so is division.)

There’s a symbol for the magnitude of V, and that’s to surround the vector by pairs of vertical lines, like this:

∥V∥

If you’re looking at a diagram, you can measure the vector off the diagram, but if you’re looking at something like [5,-12] how do you know its magnitude?

The answer is you square every element, add them together, and take the square root.

In this case, you’ll want the square root of 5•5 + -12•-12. Doing the arithmetic, you’ll want the square root of 25+144=169, which happens to be 13. So ∥[5,-12]∥ = 13.

This also works in three dimensions, consider [3,4,12], whose magnitude is the square root of 3•3+4•4+12•12 = square root of 9 + 16 + 144 = square root of 169 = 13 (again).

If you noticed something eerily familiar about this, that’s because this is also the Pythagorean theorem, the one about the square of the lengths of the legs of a right triangle equaling the square of the length of the hypotenuse. This makes sense, because the individual pieces of a vector are at right angles to each other.

Now that you have your magnitude, you can divide your original vector by it to get a unit vector. So [5,-12], turned into a unit vector is [5/13, -12/13]. That vector has a length/magnitude of 1. A more common example is [3,4] which has a magnitude of 5. The unit vector is a nice tidy [0.6, 0.8].

So a unit vector corresponding to some vector V is V/∥V∥. Usually physicists and mathematicians will write the letter with a “hat” on it (for example, Â) to denote it’s a unit vector, but unfortunately not every letter has a version with a hat on it available in unicode (at least not on this machine), so I’m a bit constrained here. You might have to get used to the V/∥V∥ long form.

So let’s get back to gravity. We have the formula for the magnitude, how do we turn that into a vector? We multiply by some unit vector. Which unit vector? The one pointing in the right direction of course. (OK, smartass, what’s that?) We know that the direction of the force on an object due to gravity is towards the attracting object.

Let’s call the force by body 1 on body 2 F₁₂. (Note the order of the subscripts, the first is the attracting body, the second is the attracted body.) The direction of that force is from body 2 back to body 1. So you can draw a vector, r₂₁ from body 2 to body 1, unit-ize it, and you have your unit vector.

Actually, typically the vector is drawn from body 1 to body 2, the opposite direction, so we will write the formula in terms of r₁₂. That vector is simply the opposite of the first one, it’s equal to -1 times the first vector.

r₁₂ = –r₂₁. Which of course means that r₂₁ = –r₁₂.

So we can write our vector version of Newton’s Law of Gravitation at last. (Edit: found an r-hat character!)

F₁₂ = -(Gm₁m₂/r²) ȓ₁₂

Notice the minus sign, which points the force vector back at the first object.

Energy

OK, so now we’re ready to proceed on to the subject of energy.

This is actually a concept that turns up again and again (and again, and Joe Biden didn’t win), in many different forms, the most basic of which is “work.”

Work, to a physicist, is what is done by a force acting on a body through a certain distance.

If I push on some object (on a frictionless surface, or out in space) and it moves some certain while I’m doing it, the work I’ve done is equal to the force I applied, times the distance.

W = Fd

Note that the distance traveled might not be due entirely to the push I gave the object. If it was already moving in that direction before I pushed on it, I’m still doing work on it by applying a force to it, even if most of the distance it traveled while I was pushing was due to the speed it already had.

(The key words are “in that direction”. If it’s moving at a 90 degree angle to the push I gave it, it has zero effect on the work done. I will have lots more to say about this, further on.)

So as a scalar, that’s just Work = Force x distance. But force is measured in Newtons or kg•m/s². Working with metric units, that’s N•m, pronounced “Newton meters.” You can break it down further, since a Newton is a “kilogram meter per second-squared”, multiply that by “meter” again for the distance, and show that a “Newton meter” is also a “kilogram meter squared per second squared:

Work is measured in: kg•m²/s²

This is another named unit, the Joule, after James Prescott Joule, who in the 1840s performed a number of experiments showing that the sorts of energy we’re talking about today could be converted to heat (more on that later). The Joule in fact is the standard metric unit of energy.

So here’s a simple example. On Earth, a one kilogram object falling one meter, has 9.8 Joules of work done to it by the force of gravity. Let me back that up with the math. The force of gravity on that one kilogram object must equal its mass times the acceleration (F=ma); the acceleration due to gravity on Earth is g = 9.8 m/s². (Little g is often used as a symbol for Earth gravity. Don’t confuse it with Big G, the gravitational constant or fudge factor from the first post in this series.) The mass is 1kg, so multiplying 1kg•9.8m/s², the force is 9.8 Newtons, pointing straight down. (In fact, “down” is defined as the direction gravity pulls, so no coincidence.)

This is acting on the object over a distance of one meter, straight down, so it’s 9.8N x 1m = 9.8 N•m = 9.8 J.

It’s not just gravity. As alluded to earlier, you can push on an object, a rocket can push on an object. So long as it moves in that direction while you’re doing it, you’re doing work.

If you start at a standstill, and continuously apply the same force to an object, its acceleration stays the same. F=ma, or more to the point, a=F/m. The distance covered, d is equal to ½at² (where t is the time you spent pushing it).

d=½at²

So if a is one meter per second per second, after you’ve spent one second applying the force, you’ve moved that object half a meter (½•1 m/s² • 1•1s² = 1m) = 1. After two seconds, you’ve moved the object two meters (½•1 m/s² • 2•2s² = 4/2 = 2m). After three seconds, you’ve moved four and a half meters (½•1 m/s² • 3•3s² = 9/2 = 4.5m). And so on. Basically, in this case square the number of seconds and divide by two.

If your object has a mass of one kilogram, the work done in the first second is 1m/s² x 1kg x 0.5m = ½ of a Joule. In the second second, though, you travel one and a half meters (bringing the total up to 2 meters). So now the work done in that 2nd second is 1m/s² x 1kg x 1.5m = 1½ Joules. So it seems like the longer you push the more work you do every second!

That moving object is now moving at 2 meters every second. And you’ve dumped a total of two Joules into it, working on it.

After three seconds, the total is 3 meters per second, and the work is 4½ Joules.

The work you’ve done on the object is manifesting itself as motion. Work is a form of energy, so is motion. Both are measured in Joules.

So let’s look at this again, cumulative totals:

t = 1 s d = 0.5 m speed = 1 m/s work done and KE = 0.5 J.
t = 2 s d = 2.0 m speed = 2 m/s work done and KE = 2.0 J.
t = 3 s d = 4.5 m speed = 3 m/s work done and KE = 4.5 J.

Notice the KE and speed match up like this: KE = ½v². But actually, that doesn’t account for the mass. If you were to push a 2 kilogram mass with twice the force, the acceleration would be the same, but the work would double, and the kinetic energy the work does would also double. So the correct formula is:

KE = ½mv²

OK, a quick sanity check. I’m saying that kinetic energy and work are both forms of energy. One way to check that, is to look at the units. Actually, more precisely, the dimensions (distance, mass, time, rather than meters, kilograms and seconds). If the dimensions are different, they can’t be the same thing.

So: Work is force times distance. Force is mass times distance divided by time squared. So, combining, work is mass x distance / ( time x time ) x distance, or more compactly, md²/t².

And kinetic energy is mass times speed squared, speed is distance over time, so combining, KE is mass x distance x distance / ( time x time ). Gathering things together, it’s md²/t².

They match, so they could be equivalent.

And indeed they are, though I won’t be proving that here!

One thing I haven’t mentioned is whether energy is a scalar or a vector. It happens to be a scalar.

OK, let’s go back to that other 1kg object, the one that fell one meter and thudded onto the ground.

Let’s lift it back up one meter, back to where it fell from. Let’s do it smoothly.

While the object is being lifted, its speed does not change. Which is to say, it’s not accelerating. So the net force is zero.

But we know that gravity is always pulling down on that kilogram with a force of 9.8 Newtons. So for the net force to be zero, we must be applying a 9.8 Newton force upward.

Since we’re lifting the object one meter, the work we’re doing on it is

W = 1m • 9.8N = 9.8 Joules.

None of this is kinetic energy, though. What happened to the hard work? I’ll tell you presently.

In this specialized case of working against gravity, you can use a fairly simple formula for the work done:

W = mgd

Where g is the acceleration due to earth’s gravity, m is the mass, and d is the distance. But that’s not quite right.

To see why, let’s go to another scenario.

You’re pulling an object, say a hundred kilograms, up a very slick (frictionless) ramp (you’re doing this because lifting the dang thing straight up is hard!).

And you’re doing it smoothly, like with the lift of the one kilogram object, neither accelerating nor slowing down on the ramp.

If the ramp is 2 meters long, can’t you go back to your formula and figure out the work?

W = mgd
W = 100kg • 9.8 m/s² • 2 m = 1960 J.

But that seems wrong. What if the ramp is almost flat? Versus a ramp that is almost vertical? If those are both 2 meters long, the vertical ramp is obviously more work!

If the 2 meter ramp is at a 30 degree slope, it turns out that the top end of it is 1 meter higher than the bottom end. (Thirty degrees is a “magic angle” in trigonometry. And if that means nothing to you just ignore it, as I’m trying to avoid trigonometry in these articles.)

Intuitively, what matters is the vertical distance traveled. Not the horizontal distance. And if you think about what work is, it’s applying a force. No force is being applied in the horizontal direction, because the object isn’t speeding up or slowing down and there’s no external force in that direction either, gravity points Straight Down.

So you need a way to take your motion as a vector, and use only the component of the motion vector in the same direction as the force to compute the work.

Because your motion and the force you’re countering are both vectors.

So what is the vertical height of the ramp? I just told you, it’s 1 meter. So 1 meter times the force of gravity gives you the right answer.

But there’s another way to analyze this! In fact, it’s probably a bit better. You could instead take the component of the force of gravity, in the direction of the slope of the ramp! After all that’s what you’re actually countering by pulling on the rope.

Note in red, the vertical vector is now broken down into an up-the-ramp component and a perpendicular-to-the-ramp component. Because 30 degrees is a magic angle, I know the force up the ramp is half the total, or 490N.

Now it is entirely appropriate to use the 2 meter length of the ramp, because it’s in the same direction as the force you are applying. 2m x 490N = 980J of work.

This is why ramps are useful, by the way. You can counter the force of gravity by applying very little force. In this case, half as much. The price you pay is you have to apply that force over greater distance, in this case twice as much. You could reduce the force as much as you want, if you have room and material for a longer and longer ramp.

Dot Products

Gee, it’d sure be nice if you could do this computationally. Well, you can. You can do trigonometry to determine that 1/2 factor for 30 degrees, or whatever it is for any other angle.

Gee, it’d sure be nice if you could do this computationally, without trigonometry. (After all, you don’t want to have to pester a geek and OMG! make him feel useful doing the trig for you.) Well, you can, if you have the vectors!

We do have them. The force we have to apply is [0, 980]N. The amount of distance is 2 meters, but we need the rise and run from the first diagram to be in vector form: [1.732, 1.0]m

[Trivia note: 1.732 is the square root of three (rounded to three decimal digits). Like I said, 30 degrees is a magic angle, the legs with a hypotenuse of 2 are 1 and sqrt(3). It’s easy to remember the square root of three because its digits spell out Washington’s birth year, 1732. If you’re a coin geek you can remember that because the Washington Quarter we use today began to be issued in 1932, his bicentennial. If you’re just a regular geek, you probably don’t know Washington’s birth year, but you probably do have 1.732 memorized and can use it to remember that Washington was born in 1732.]

OK, we have our two vectors, F=[0, 980]N and d=[1.732, 1.0]m

Here’s what you do. Multiply the first elements together, then the second elements, then the third elements (if you’re working in 3D), and if you’re playing 64 D chess, do the same for elements 4 through 64. Just keep going until you’re out of vector.

In this case, I end up with first elements: zero, and second elements: 980N•m. Done.

Add those numbers (all two of them here, all sixty four of them if you’re Donald Trump) and get, 980N•m.

You didn’t have to do any trigonometry! You didn’t have to break the vectors down into components, not in x-y or even along some cockeyed slant!

What we just did was to take the dot product of the two vectors, in other words we computed F∙d. That’s the real, vector form of the formula for work.

W = F∙d

Now I sometimes use a dot to show multiplication, particularly when I’m showing multiplying two actual numbers, or units. I’m having to use a big fat dot here, to distinguish the vector dot product from the just ordinary multiplier dot. (Note: It shows on my computer doing edits in a file, it isn’t showing up in the post editor, and may not show up as a big dot when it posts. We’ll find out, sometime before you read this!)

There are two things you may have noticed.

One, I’m talking about the dot product, not just the product; as if there were some other kind of product. With vectors, there is. Don’t worry…you’ll find out some future week! (Evil laugh!)

And another thing…the result of a dot product, is a scalar.

Work is a scalar. Kinetic energy is therefore also a scalar. Energy has no direction.

OK, let’s have a little more fun with the dot product. Take some vector, like v = [3, 4, 12]. Let’s take the dot product of it with itself, v∙v

That’s 3•3 + 4•4 + 12•12.

Does this seem familiar? Like maybe we did the exact same thing earlier in this marathon of post, while figuring out the magnitude of that exact same vector?

Except that when getting the magnitude we went on to take the square root. With the dot product we don’t do the square root. So the dot product of a vector by itself is the square of the magnitude. So, here’s a rule:

For any vector v: v∙v = ∥v∥²

Another rule. If two vectors are perpendicular, their dot product is zero!

I’m going to make up a four dimensional vector off the top of my head (I promise, I just made it up off the top of my head):

[12, -7, 9, -15]

I can make up another four dimensional vector and know that it’s perpendicular to this one, without having to draw a diagram. Which is good because my supply of four dimensional paper is a bit low right now. (The COVIDschina has caused all kinds of supply chain havoc.)

OK, let’s just make the first element of the second vector 9, and the second one 9 as well. You could literally pick any numbers for all but the last one. Make the third element -20. Let’s hold off a bit on the fourth one, and call it x.

[9, 9, -20, x]

I can take the dot product of this, it’s 108 + -63 + -180 + -15x, combining I get -135 + -15x, which has to equal zero if the vectors are to be perpendicular. It turns out if the last element is -9, the last bit of the cross product is +135 and the total is zero. (I was lucky, I didn’t end up having to multiply by an ugly fraction at the end.)

So even though I can’t draw a diagram of these two vectors, I know, like I know that 2+2=4, that [12, -7, 9, -15] and [9, 9, -20, -9] are perpendicular, because their dot product is zero.

If two vectors are parallel, but of different sizes, the dot product will be the product of their magnitudes. For example, [3, 4] and [6, 8] are parallel, because the second one is just 2 times the first one. Take the dot product, 3•6 + 4•8 = 18 + 32 = 50. If you do Pythagoras on those two vectors, their magnitudes are 5 and 10, which multiply together to make 50.

And that’s as far as I can take you without trig. There is a rule that tells you how big the cross product will be in terms of the two vector magnitudes and the angle between them…but, trig. (Fortunately the geeks here who know trig probably already know the rule.)

Potential Energy

OK, let’s return to the 100 kilogram block we pulled up the ramp, lifting it a meter, doing 980J of work.

In this case once we stop lifting the object isn’t moving. So our work didn’t become kinetic energy. What happened to it? It became potential energy. It’s basically stored in the object, as if it were a battery. To get it back, we drop the object, pretending to do so on some deserving Deep State puke’s head. (Maybe we can lay their picture flat on the ground.)

On earth, at least, we already have a formula for potential energy. It’s the work we put into it, the mass times the acceleration due to gravity times the distance. Only instead of d let’s use h for height, because that’s in the same direction as the force.

PE = mgh

where h is the height above the ground. Its distance times force, and force is in turn mass times acceleration due to gravity, g (9.8 m/s²).

So the object has potential energy. If you want the kinetic energy back, drop it, but then the object is back on the ground and the potential energy is gone.

(Note that we’ve been behaving as if the ground is the place where potential energy is zero. In fact, your choice of where zero is, is completely arbitrary. Imagine dropping the object down a well. If the potential energy is zero at ground level, it’s actually a negative number at the bottom of the well. As it turns out physicists like to put the zero point at infinity, and you’ll see why in a moment.)

It’s almost as if you can swap kinetic and potential energy freely.

Indeed, in many circumstances you can. If you don’t have to deal with friction, and other objects getting in the way, you can do it. One place where this is true is in space, there you only have to deal with gravity. In our discussion so far we’ve ignored everything else, so it won’t be quite accurate–you won’t quite get all the energy back when you drop the object, because of air resistance, no ramp is frictionless, and so on, but in space, there actually is nothing else.

An object’s kinetic energy, plus its potential energy, put together are called the mechanical energy and in space, for some given object in orbit, this is a constant.

So let’s look at kinetic versus potential energy in space.

Kinetic energy, we know how to deal with. But there’s a bit of a wrinkle with potential energy. On earth we deal with lifting an object a short distance, and the force of gravity is effectively constant over that distance. But when in space, you are not dealing with a constant force. Gravity measurably weakens the further you get away from Earth. So PE=mgh won’t work as a formula for potential energy. Instead, when dealing with potential energy with respect to the Earth, it’s –mm_eG/r, with m_e being the mass of the Earth, G being the gravitational constant/”fudge factor” and r being the distance from the center of the earth. And as always, our object’s mass is m. If r is set to infinity, the potential energy is zero. As you get closer to the Earth, the number becomes more and more negative, reflecting less and less potential energy. This formula is only valid above the surface of the earth. Below the surface gravity again decreases. If the earth were a point mass, the formula would be perfect (and the Earth would be a black hole).

m_eG is also known as μ_e, the gravitational parameter of the earth, and that is 3.98×10¹⁴ m³/s². So our potential energy formula is now:

PE = –mμ_e/r = – 3.98×10¹⁴ m/r

The earth’s radius is 6,378 km (through the equator, not elsewhere, but let’s use it), that’s 6,378,000 meters. So at the surface of the earth, the potential energy of a one kilogram object will be -62,402,000 Joules.

So it stands to reason that if you can give a one kilogram object 62.4 million Joules of kinetic energy, it will keep going until it’s an infinite distance away, having traded all of its kinetic energy for potential energy and bringing the potential energy up from looking like a millionth of the national debt all the way to zero.

Whatever that speed is, it’s the escape velocity of Earth. Impart it to an object on the surface, and it ain’t ever coming back!

Remember:

KE = ½mv²

But this time we know the kinetic energy and we want the velocity. So doing a bit of rearranging:

v² = 2 KE/m

So simply multiply the 62.4 million Joules by two and divide by our mass of one kilogram, then take the square root. The square root of 124.8 million is 11,171.4 meters/second. That works out to 6.94 miles per second. And that’s our escape velocity, at least as seen from the surface of the Earth.

You can do this whole thing again with, say, a 57 kilogram object. The potential energy on the surface is 57 times as much (a bigger negative number), the KE is 57 times as much, but you divide out the mass. So the escape velocity is the same.

Now, let’s consider an object in a perfectly circular orbit. It will have a certain potential energy. It will also be moving at a constant speed. The sum of the potential energy and the kinetic energy, therefore will remain a constant.

But this is true in an elliptical orbit, too!

With an elliptical orbit, one end of the ellipse is as far away as the orbiting object ever gets away from Earth (the apogee, or more generically for any body, the apoapsis), the maximum potential. The other end is as close to the Earth as the object ever gets, the perigee or periapsis. It has a lower potential, which means the kinetic energy must be higher to make up for it. And indeed, if you’re in an elliptical orbit (around anything) you will speed up the closer you get to the object you are orbiting.

And in space, with no friction and no objects getting in the way, provided nothing comes along and disturbs that orbit, the object will go on circling, swapping potential for kinetic energy and back again, with perfect efficiency, forever. The mechanical energy, PE + KE, equals some constant. In fact, it’s zero if the object is moving at escape velocity, since PE + KE cancel each other out perfectly at that speed.

Something that doesn’t occur to most people. If the mechanical energy is zero, it will always be zero, and the object is always moving at escape velocity, no matter how far away it gets from Earth; it’s just that escape velocity is lower the further away you get. It also doesn’t matter which direction it’s going. It could even be going almost directly towards Earth. It’s still never coming back, as long as it doesn’t come so close to Earth that it collides with Earth. The one other thing you can say is that the path it traces will be a parabola.

When someone asks “what’s the Earth’s escape velocity?” they almost certainly mean “at the Earth’s surface.” So give them that 11 thousand something. But it’s different if you’re already ten thousand miles up!

If the mechanical energy is greater than zero, it’s not only going fast enough to escape Earth, it’s got surplus velocity to boot. (And it will travel in a hyperbola.) If the mechanical energy is less than zero, it will eventually reach a maximum distance and start coming back. It’s in a closed orbit, which will be an ellipse of some kind, a circle being the limiting case (all circles are also ellipses). The lower the total energy, the smaller the ellipse.

So under a certain idealized set of circumstances, mechanical energy is conserved.

What about other circumstances? Mechanical tends to bleed off, and decrease, especially that part of it that is in the form of kinetic energy. Think of a pendulum, that’s another “ideal” case of swapping kinetic for potential energy; the pendulum swings fastest at its low point, and is motionless at the top of its swing for a split second. It’s clearly trading potential and kinetic energy back and forth, over and over. But a pendulum is moving through the air, and air resistance will take a little bit of speed off that pendulum, so it won’t rise quite as far on the upswing. Over and over again, the pendulum swings less and less and eventually stops. It would go on longer in a vacuum, but the pivot point introduces some friction, too.

Friction is the nemesis of mechanical energy. The more friction, the more energy bleeds out of the system (unless it has no kinetic energy to begin with, think of a rock on a mountain top).

What happens to things when friction is going on? They heat up. So mechanical energy is being turned to heat.

Heat and Chemical Energy

As it turns out, heat is yet another form of energy. Our friend James Joule helped figure that out.

Heat, it turns out, is measured a bunch of different ways. The amount of heat necessary to raise the temperature of water one degree Celsius/Kelvin is defined as a calorie; a thousand of those is a kilocalorie (kcal), or sometimes Calorie with a capital C. That “big C” calorie is what you count when you’re on a diet, a food Calorie, and since heat is energy, it turns out that a Calorie of heat is 4,184 Joules. Chemists tend to use calories and kcal because they heat water a lot, then convert at the very end to Joules. They have 4,184 memorized. (I had to look it up.) It’s easy to work with calories when dealing with water. How many grams of water times how many degrees C you heated it up.

Not only is heat another form of energy, it’s the garbage can of energy. You can convert kinetic energy into heat, like by the energy of impact heating up whatever got hit, but you cannot convert all heat back into kinetic or potential, or any other kind of energy, only some of it. So energy tends to accumulate as heat over time, and this process is not completely reversible, so eventually all energy in the universe will be unharnessable heat. This is a consequence of thermodynamics. We’ll be out of usable energy. That is an energy crisis! Fortunately this is trillions of trillions of years off in the future, so you’d better do your taxes, but still, thermodynamics is the real “dismal science” because it tells us the universe is running down. You can’t win, you can’t break even, and you can’t quit the game.

This is also why any generating plant that relies on heat is not perfectly efficient. You burn the coal to heat the water into steam, you use the steam to turn a generator…but you can’t harness all the energy you put into the water and turn it into electricity, because that energy is all heat. Some is lost to practical use…forever. In fact a coal plant engineer would do cartwheels down the hall if he could get the plant to 35% efficiency. Two thirds of every pound of coal burned is wasted.

There is also energy in chemicals. That should be obvious by now since food contains kilocalories. Obviously, you can get that energy out by burning things. But it comes into play in another way. If you are James Comey, and you finally got your comeuppance and you’re having to make little ones out of big ones while waiting for your date with the executioner, you’re taking a big honkin’ sledge hammer, giving it a lot of kinetic energy, and smacking it into a rock, which breaks.

It take energy to break a rock. And that’s because the rock is full of chemical bonds that have to be broken, that’s a facet of chemical energy. The rock lost energy being formed, you’re resupplying it to break it back apart.

And when you eat bacon, you end up “burning” a lot of that fat for energy, and that is a chemical process.

A huge part of chemistry is tracking the energy through chemical reactions, supplying some where needed, using it where it’s given off. And reactions that give off energy and leave the reactants with less total energy tend to be favored; chemicals like having very little energy bottled up inside them. (There are plenty of added complications here; I won’t trouble you with them, but they are the reason paper doesn’t just burn spontaneously at room temperature.)

Conservation of Energy

OK, let’s take these other forms of energy into account (and others I haven’t even mentioned). What then?

You find that energy is conserved. In a closed system it is never created from nothing nor is it destroyed, though it can be converted from one form to another. So we have our third conservation law. We now have mass, momentum and energy conserved.

And that is another part of the state of physics in 1895.

Potential

I want to drop one more concept on you. The concept of potential. Not potential energy, just potential.

Consider a rock at the top of a cliff. It has a decent amount of potential energy, right? Another rock right next to it twice as massive has twice the potential energy. Or you could find a rock of the same size on a cliff twice as high. The point being that the potential energy depends on the vertical distance and the mass of the object.

Sometimes it’s very convenient to divide by the mass. When you do that with potential energy, you get potential energy per unit mass, also known as specific potential energy, or just plain potential. The two rocks at the top of the same cliff have the same specific potential energy, the same potential. But the rock at the top of the other cliff has twice the specific potential energy, because the cliff is twice as high.

You can turn potential into “how fast will that rock be going when it hits the ground, if it falls off the cliff” because that does not depend on the mass of the rock. Gravity accelerates all things equally, because the more massive the object, the more the force increases.

And with orbital mechanics, the satellite is usually such a tiny fraction of the primary’s mass, we divide the mass out of everything, turn the forces into accelerations, the potential energy into potential, and just square the velocity and divide by 2, because the mass of the satellite never changes, and if it does, so do the forces on it, it’s kinetic energy, and potential energy all in proportion. You’ve seen a hint of this in g being the acceleration due to gravity, not the force due to gravity. It’s more convenient to work with since the mass really doesn’t affect velocity, acceleration, or position.

I didn’t bring this up gratuitously. Potential will turn ot to be an important concept down the road, particularly when we look at electricity.

OK, now on to our 1895 mystery:

What makes the stars shine? (Introducing Power)

This is a big one. Almost everything we can see in the universe is a star. The planets here and out there are an insignificant fraction of the visible matter in the universe.

So if we can’t figure out the stars, in one respect we don’t know Jacques Schitt (or Adam Schiff) about the universe.

OK, so let me try to summarize what they had figured out in 1895. The stars shine, actually, because they’re hot. In the same way that embers in a fireplace glow. But stars are much hotter, the light they put out is whiter (true even for “red dwarfs”), and they put out a lot more of it. Physicists had done work on this “black body” radiation and could describe it really well, though they couldn’t figure out just yet why stars (and embers) didn’t radiate more at even higher frequences (bluer light and even ultraviolet)

But something that is glowing because it is hot, is actually shedding heat that way. Eventually it will cool off, stop glowing and assume ambient temperature.

So really, the question is what makes the stars continue to shine.

And that is a very good question. In order for a star to not just go dark, it must be accessing the same amount of energy every second that it puts out in that second. If it’s getting less energy, it will start to cool off, if it’s getting more, it will heat up. Most stars are fairly stable, so there must be a balance: energy radiated must equal “fresh” energy used to heat up the star.

We are talking about a rate of energy consumption, naturally expressed in Joules per second (J/s). That, folks, is power, and is measured in Watts. Yes, the Watts you know from light bulbs. Chances are good you didn’t know Watts are a metric unit!

The sun, to take a well known example, is pumping out 3.828 x 10²⁶ watts. It’s doing so in all directions, so our little dinky Earth 150 million kilometers away gets only a minuscule fraction of it. Some of it hits other planets, the rest just blasts off into space, a ridiculously tiny fraction of it will hit other stars and their planets and maybe be seen by aliens.

Where does the sun get the 3.828 x 10²⁶ Joules it needs every second to sustain this?

Let’s go over the possibilities that people had come up with. Chemical energy? What if the sun were a gigantic sphere of coal and it were being burned?

Well, we know how big the sun is, and we know its mass. We know how much energy coal releases when it burns. (We know that very well, since our economy largely depends on it.) If the whole thing were coal and were burning to pump out that kind of wattage, it would last 1500 years.

Which means the sun wouldn’t last the span of time since the fall of the Western Roman empire. Well, we have daylight now, and had it back then, so…scratch chemical energy. There are things that release more energy than coal, but not that much more; we can’t get from the pyramids to today.

But we already know kinetic energy can turn into heat, so what if a lot of meteors are hitting the sun, continuously? As it happens, if 1.2 x 10¹⁷ kg of meteorites were to hit the sun at its escape velocity every second, that would be enough to do it. That’s 120 trillion tonnes of stuff, every second!

But there’s no evidence that there’s that much junk hitting the Sun. Some of it would surely hit Earth and meteor strikes would be a lot more common than they are. Besides, this much mass falling on the sun would add one percent to its mass every 300,000 years. Increasing the mass of the sun increases its gravity, and we, monitoring planets orbiting the sun, would definitely know if this were happening, because the planets would gradually get closer to the sun and speed up in response to the mass change. Each year would be two seconds shorter than the year before, and there’s no way we’d miss that.

Finally, the best suggestion…though not good enough…came from Herman L. von Helmholtz in 1853. He was one of the people who first formulated the law of conservation of energy, so you can be sure he took that into account when making his suggestion. Why use meteorites, when the sun itself could be contracting and not gaining mass? If the material at the surface of the sun is in fact still falling towards the center, it’s converting potential energy to kinetic energy which can heat the sun up.

Helmholtz calculated that if the sun were shrinking 0.014 centimeters every minute, that would actually release the energy needed.

That works out to a mere 560 miles (out of a total diameter of 864,000 miles) in the roughly 6000 years of recorded human history, and again, this does not involve altering the mass of the sun at all. That total is a lot less since the invention of the telescope; small enough we could not have measured it as of 1895. (We’ve had more time since then, and our tech is better. Maybe we could do it today.)

So it looks promising. But running the clock backwards, the sun would have been big enough to swallow up the earth in its orbit at some time in the past, and that was calculated to be 18 million years ago. That’s a maximum age for the sun and especially the Earth, if that’s how the sun gets its energy. If it were any older than that, Earth wouldn’t exist today.

And that’s not nearly long enough. Geologists had plenty of compelling arguments that the earth must be hundreds of millions of years old, if not billions. And evolution needed time to act too. The theory had been put forward in 1859, and biologists were becoming convinced. Those were two independent arguments against a less-than-eighteen-million-year-old Earth.

So we have astronomers saying the sun can’t be that old, and geologists and biologists saying it must be that old. Who was wrong? Well, there was tangible evidence for the old earth, against physicists and astronomers not knowing how it could work; they were basically arguing from ignorance, and they knew it.

So they were willing to believe it was old, but that meant they had no idea what was powering the sun.

And that applied to all the other stars in the universe, too.

What’s powering the sun and every other star in the universe?

No one had any real idea, as of 1895. And remember, most of the visible universe is stars, and we didn’t understand them, so we really didn’t understand much, on a weight basis.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

To conclude: My standard Public Service Announcement. We don’t want to forget this!!!

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!