William M. Briggs

Statistician to the Stars!

Page 4 of 408

Evolution Under Fixed Constraints; Or, Why Random Changes Don’t Cut It

Not actual human beings.

Not actual human beings.

See if this analogy makes sense. A ramp onto which you loose a ball, which can roll down and fall into one of three slots. The configuration is such that the ball must go into one of these slots. It cannot get stuck or jump off the ramp. Suppose, like a pachinko machine, the ramp is covered in plastic to prevent leakage.

Now something will cause that ball to go into one of the three slots, but suppose you’re no expert in physics and can’t figure out the equations of motion. So you don’t know the cause.

But can you agree with me that the ball must go into one of the three slots? As a matter of logic, or information, given the setup, the probability of any slot is 1/3. The probability didn’t cause the ball to end up anywhere; chance isn’t a cause. That the ball could potentially be in one of the slots also wasn’t a cause.

Randomness isn’t a cause, either. Neither “chance.” The ball did not fall “randomly” in any causal sense. It fell because of the physics; our ignorance of the physics means nothing.

The ball had to go into just these three slots. Why? Well, that was the way the setup was designed.

And there it is. The “D” word.

The system from its start to its end could be said to have evolved. Evolution in action! But it could have only evolved in certain set ways. The ball could evolve only into one of three configurations. It could not have evolved into fourth slot, for one doesn’t exist. It could not have evolved into a petunia.

This is a stretch of the word evolution, however, which is why it is only an analogy. But ordinary evolution cannot be different in manner, though of course it differs in mechanism.

When DNA undergoes a mutation it must do so only in certain constrained ways. Like the ball, it must fall into prescribed “slots.” Some thing or things will cause the mutation. Nobody might know these causes, or even the range of possible “slots”. This ignorance is called “randomness”. But randomness isn’t ontological. There is nothing physical there.

These facts are why explanations of evolution are often screwy. Take this example from The Scientist:

Are mutations truly random?

Do genetic mutations really occur at random spots along the genome, as researchers have long supposed? Maybe not, according to a study published online today (January 13) in Proceedings of the Royal Society B, which proposes a mechanism for how new mutations might preferentially form around existing ones.

Truly random has no physical or biological meaning. Here it seems to be a stand in for uniform. Whether mutations are uniform along a genome, or express a preference for other sites, some thing or things still causes each one, and under some constraints. It is the duty of the biology to discover whether these causes are biased towards this or that direction. That is, what the “slots” are and their natures.

Another frequent mistake is made by those anxious to argue evolution is “unlikely”. For example, the paper The Mathematical Impossibility Of Evolution by Henry Morris, Ph.D. Morris’s argument is along the same as we met yesterday, when a fellow calculated the probability you existed was nearly impossible.

All probability—a measure of our information—is conditional on the premises supplied. Change the premises, change the probability. Morris starts with the central error of his opponents, “Mutations are random changes in genetic systems”, as if randomness is a cause, from which he concludes “Since random changes in ordered systems almost always will decrease the amount of order in those systems, nearly all mutations are harmful to the organisms which experience them.”

This is a theoretical conclusion, not one based on observation. (I recall people used to say bumblebees couldn’t fly because aerodynamical theory forbade it.) It seems to also be based on the premise that random is not only a cause but also uniform in action. That would be like saying that while we can only see three slots, theory demands there be four thousand (maybe there are slots besides the three which are too narrow, but which theory insists are options).

Just like “you exist” cannot be that impossible since you, in fact, exist, evolution cannot be impossible because it, as observations prove, exists. The nature of evolution is badly misunderstood on both sides.

We still have not succeeded purging the mysticism of randomness from probability. Frequentist statistical theory is rife with it. But then so are many interpretations of quantum physics.

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I was reminded of this after popping over to Mike Flynn’s place and seeing this and this. Travel day today and tomorrow.

The Probability Of Your Existence

Typical college student.

Typical college student.

To the nearest order of magnitude, there have existed, including us, about 100 billion human beings. This proves what was always, until our day, quite obvious: that people are good at breeding. (Or were, before discovering contraception and abortion, of course.)

That’s a lot of people in a relatively short period of time, geologically speaking. Humans have only existed some few hundred thousand years.

According to Harvard Law blogger Ali Binazir, author of Awaken Your Genius, you, dear reader, only have a “1 in 102,685,000” chance of existing. Pretty small, no?

But since there’s been so many of us, each one of us being next to impossible, something has gone wrong in the calculations or our thinking.

Nothing better illustrates the truth that all probability is conditional than Binazir’s calculation. It’s sort of a Drake equation for individual human existence. The Drake equation is a probability-like calculation which gives the chances of other life forms like us, i.e. rational, existing on other planets. It is notorious in its liquidity: it won’t stay solid. Binzair’s calculations suffer from the same flaws: he’s unable to keep straight which side of the equation he’s on.

Given you’re reading this post, the probability you exist is 1, i.e. it is certain. That’s because there must be a you to read. But Binazir tells us that the probability you exist is a number nearly equivalent to 0, the other end of the probability spectrum. Both probabilities can be right, since all probabilities depend on the premises used. Depends on the meaning of “to exist”, also. Does it mean “being made” or “alive and functioning now”?

Alive and functioning now is easy: you exist certainly. But how did you get made? Well, mom met dad and they did what came naturally. Out came you. You, logic insists, could not be other than you. This is necessary to emphasize.

The probability your parents had any kids is also 1, because you are one of them. But the probability that two mated humans reproduce is different. That probability doesn’t exist because no premises have been specified. One possible premise: both over 80 years old? Another: one is sterile, by natural or artificial means. Another: one is forever on the road. And on and on.

Now each time the mates attempt to reproduce, either a baby is produced or it isn’t, a tautology. In either case, something caused the baby to be made or to stop it from being made. We (typically) won’t be in the position of knowing these exact causes, so we say the creation or lack of it is “random”, which is just another label of our ignorance of the causes. But if we assume these causes are “regular”, and are careful to specify the kind of mates to which they apply (say, 20-30 year-olds, of this and such background, etc.), then we can use probability to express our incomplete knowledge and make reasonable predictions over groups of mates.

In any case, we are not asking what is the probability your parents had kids, because they obviously did. We asking the probability of you yourself coming into being. Assuming each of your mom’s and dad’s gametes were unique (are male gametes like snowflakes? has anybody checked? I ask in ignorance), then each mating could make a different baby. But each mating will have a list of causes which either make or stop the baby. So again we’re not talking about what causes the individual gametes to meet.

What premises to use? Any individual attempt? Thus the number of male gametes and a fixed female gamete. In ignorance of the causes, and assuming conception, there are n male gametes and one female, thus the probability is 1/n that this male gamete meets this fixed female one. Is that newly created baby you or somebody else? Assuming no conception, then no you and no anybody either. What is the probability of no conception? Well, what premises do we assume?

You can see this is getting nowhere slow.

The problem is in the question. What is the probability you exist? This is not what is the probability somebody else exists, or the probability somebody in your place exists. It isn’t even the probability some other human exists—which is one by the plain meaning of the question. Why? Because people exist.

You exist, too. Therefore it must be the probability you exist is 1. That you might not have existed is a counterfactual question, which is perfectly comprehensible as long as we supply the premises under which you would not have existed. Say, you imagine your dad got called away on a business trip during the time in which your parents conceived you. Or that your dad never met your mom. Then, given those premises, the probability would not have existed is also 1, because there would have been no causal way of you coming into existence.

Face it. Probability is never as easy as you hope it is.

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Thanks to The Carolina Cowbody for suggesting this topic.

Summary Against Modern Thought: Non-existence Of Infinite Causal Chains

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles.

Previous post.

Here’s what was proved so far: (1) that some things move and others change, and that (2) whatever is in the process of being moved or being changed is being moved or changed by another. Utterly unremarkable assertions; but both the backbone of science, even though some scientists pretend to be skeptical of causality. There is a world, nay a universe, of difference between our knowledge of a cause and of the existence of a cause. Poor Jaki spent his career reminding people of Heisenberg’s fallacy of equivocation. “Poor” because, for whatever reason, people cannot keep in mind the difference between epistemology and ontology. Once more I beg you to read the stone being moved by the stick being moved by the arm being moved by the muscles etc. example. Today we reach the end of the First Way. Next week we begin the Second way.

Chapter 13: Arguments in proof of God’s existence

4 This argument contains two propositions that need to be proved: namely that whatever is in motion is moved by another, and that it is not possible to proceed to infinity in movers and things moved…

11 He proves the other proposition, namely that it is impossible to proceed to infinity in movers and things moved, by three arguments.i

12 The first[10] of these is as follows. If one were to proceed to infinity in movers and things moved, all this infinite number of things would necessarily be bodies, since whatever is moved is divisible and corporeal, as is proved in 6 Phys.[11]ii Now every body that moves through being moved is moved at the same time as it moves.iii Therefore all this infinite number of things are moved at the same time as one of them is moved. But one of them, since it is finite, is moved in a finite time. Therefore all this infinite number of things are moved in a finite time. But this is impossible. Therefore it is impossible to proceed to infinity in movers and things moved.iv

13 That it is impossible for the aforesaid infinite number of things to be moved in a finite time, he proves thus.[12] Mover and moved must needs be simultaneous; and he proves this by induction from each species of movement. But bodies cannot be simultaneous except by continuity or contact. Wherefore since all the aforesaid movers and things moved are bodies, as proved, they must needs be as one movable thing through their continuity or contact. And thus one infinite thing would be moved in a finite time, which is shown to be impossible in 6 Phys.[13]v

14 The second argument[14] in proof of the same statement is as follows. In an ordinate series of movers and things moved, where namely throughout the series one is moved by the other, we must needs find that if the first mover be taken away or cease to move, none of the others will move or be moved: because the first is the cause of movement in all the others. Now if an ordinate series of movers and things moved proceed to infinity, there will be no first mover, but all will be intermediate movers as it were. Therefore it will be impossible for any of them to be moved: and thus nothing in the world will be moved.vi

15 The third argument[15] amounts to the same, except that it proceeds in the reverse order, namely by beginning from above: and it is as follows. That which moves instrumentally, cannot move unless there be something that moves principally. But if we proceed to infinity in movers and things moved, they will all be like instrumental movers, because they will be alleged to be moved movers, and there will be nothing by way of principal mover. Therefore nothing will be moved.vii

16 We have thus clearly proved both statements which were supposed in the first process of demonstration whereby Aristotle proved the existence of a first immovable mover.viii

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iIt is utterly absolutely painfully crucial that you understand what is meant by this. Aquinas means here-and-now, or at-this-very-moment causation. The stick moves the stone here-and-now, your arm moves the stick here-and-now at-this-very-moment, your muscles move your arm here-and-now at-this-very-moment, simultaneously. Your muscle and other cells here-and-now at-this-very-moment move, and so on down to something. Some first unmoved mover. It is this here-and-now at-this-very-moment chain which cannot proceed here-and-now at-this-very-moment to infinity. Update See YOS’s clarification on “instantaneous” movement/change below.

Ed Feser (who not uncoincidentally, since I’ve stolen many of my ideas from him, today wrote on a similar subject) has taken great pains in his many books and articles to teach that this per se chain of here-and-now at-this-very-moment causes exists here-and-now at-this-very-moment, that everything is happening at once. His experience has been that this teaching does not stick. Why? Who knows. But since it is so, I remind you we are not talking about accidental chains of causation, such as when one rock falls off a hill into another, and the second rock then hits a third, and so on. No no no no. We are talking about how movement or change in the here-and-now comes about. Meditate on the example until it is clear in your mind before continuing.

Or watch Feser’s terrific lecture on the subject.

iiAll of Aristotle’s Chapter 6 may be found here. The stick is a body, and so is your arm, and so are your cells, the chemicals, the electrons and neutrons, the quarks, the strings (if they exist) and whatever, if anything, is “below” them. Notice that Aquinas and Aristotle use a proof by contradiction. They assume there exists an infinite here-and-now chain.

iii Here-and-now at-this-very-moment!

ivSweet, no? If there did exist an infinite chain, and because we certainly see things move or change in finite time, this entire infinite chain would have to move not only in finite time, but at this moment, here and now (have we memorized this yet?). The proof immediately follows.

vAristotle proves even more than his: his book 7 may be found here. Anyway, it is clear that if we have an infinite here-and-now chain of objects, the whole thing must itself, here-and-now at-this-moment, move. And that is not possible in finite time. Worse, this would have to be the case for everything everywhere that is in the process of being moved or changed. That’s a lot of chains and lots of infinite movements! Since it is absurd that these infinite chains can move in finite time, yet things are moved or changed in finite time, the chains must not be infinite.

viIf the here-and-now chain is finite—this is an assumption, arguendo—and the first element is removed, the later parts also cannot move, which is obvious. Now I don’t think people understand how big infinity really is. It is not just big, nor even BIG, but horrifically huge. An infinite chain would have more than a googol of elements, which is 10100; it would have more than a googoplex of elements, which is 10googol. If you were to keep doing that operation, namely taking 10 to the power of the last result, and continuing once a second for a whole day, you still would not have got close to infinity. You would still be infinitely far away. But the, to us humans anyway, unimaginably long chain would have only just got started! Just to use your arm to move a stick to push a stone.

An infinite chain is one which never stops. It goes on and on and on and always on some more. If infinite chains existed, there would not and could not be a first element. How, then, would the whole thing get started? Answer: it could not. It would be impossible—not unlikely, but impossible.

I think people believe infinity isn’t all that big because of mathematical analysis, and used in many areas of science. In analysis we regularly and somewhat glibly call on infinity. We say some function converges (perhaps) “O(n2)”, meaning as the number of elements grows, the finite function gets closer and closer to its infinite cousin. We plug in n = 20 or even n = 100 and see that the function is “settling down”, i.e. approaching some obvious value, and we think, “Ah, infinity and n = 100 aren’t that far apart.” However useful an approximation our function at some finite number of elements is, it is never the real value of the function at infinity. Taking approximations as reality and not just as approximations is a common, though not usually painful, fallacy.

It’s a killer here, though. When we are talking movement or change, we cannot have an approximation. We must needs have the whole chain. Stopping at the first (say) 100 elements just won’t do. If we remove a link, the chain cannot pull. And if we do have an infinite chain, there will be nothing to give the chain impetus. Without a first mover, nothing can happen. The chain thus cannot be infinite.

viiThe rock is being moved instrumentally by the stick, which is being moved instrumentally by the arm, and so forth. The principal unmoved mover sets off the whole shebang. I think we get it by now.

viiiLet’s review. We proved the premises in this First Way:

Whatever is in motion is moved by another: and it is clear to the sense that something, the sun for instance, is in motion. Therefore it is set in motion by something else moving it. Now that which moves it is itself either moved or not. If it be not moved, then the point is proved that we must needs postulate an immovable mover: and this we call God. If, however, it be moved, it is moved by another mover. Either, therefore, we must proceed to infinity, or we must come to an immovable mover. But it is not possible to proceed to infinity. Therefore it is necessary to postulate an immovable mover.

The premises being true, and the argument valid, the conclusion must also be true. And therefore it would irrational to deny it. But why God as the unmoved mover? Why not call the immovable mover the Higgs Field Driver or whatever? Well, we haven’t fleshed this part of the proof out yet, so our modern scientistic suspicion is natural.

As a hint—and only a hint—there cannot be more than one immovable mover, one unchangeable changer. There must be something which exists which acts to sustain everything. Stay tuned!

Next installment.

[10] 7 Phys., l.c.
[11] L.c.
[12] 7 Phys. i. ii.
[13] Ch. vii.
[14] 8 Phys. v.
[15] Ibid.

Don’t Go To Confession; Humpty-Dumptying The English Language; More

Australian Anglicans unveil their new confessional.

Australian Anglicans unveil their new confessional.

A Time To Die

The play is done! But, as you can see, you cannot see it. This being the 5th of July and a Saturday in what must be a very long weekend, I decided to hold off posting it until next week when there is a better chance of people being near their computers.

Regular readers will remember that George R.R. Martin offered to accept $20,000 from any of his readers who longed to be killed off in a ghastly manner in his next novel. Not being as famous as Martin, I offered the same service for the low, low introductory price of $10.

Though the hour is late, there is still a chance to participate. Click the Donate tab at the top and I’ll find a way to squeeze you into your grave. But before you do, you’d better…

Go To Confession

But not in the Anglican Church in Australia. The enlightened leaders of that organization are now forcing priests to rat out parishioners who confess to acts which carry jail terms of at least five years.

“Forgive me, enlightened one, for I have sinned. It has been forty-two weeks since my last confession.”

“Go on, my son.”

“I accidentally side-swiped another car on my way home last week and didn’t report it.”

Sounds of pages flipping. “Were you at the time going more than 40 KPH?”

“Um, I don’t recall. Maybe.”

“Hmm….” More page flipping. “Well, was the other car moving at the time?”

“No, it was parked.”

Flip, flip, flip. “Now we’re getting somewhere. Was this on a public street or in a private lot? Such as might be found at a Drake’s Supermarket?”

“Right on the street.”

“One final question. Were you drinking at the time?”

“Well, I might have had one or two beers at the pub. But I was fine to drive.”

“My son, according to the Criminal Code, if you’re found guilty—and you have just confessed to the crime, so that is not really in question—your offense has a maximum sentence of six years. I’ll be sending a recording of this conversation to the police. Slide your ID through the slot. I’d advise you not to attempt to flee. That can add considerably to your tariff…”

Confession no longer means what it used to mean, and this is because of…

Humpty Dumpty’s Revenge

‘When I use a word,’ Humpty Dumpty said, in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’

How many remember Carroll wrote Alice as a parody of intellectual insanity? Never mind. Satire isn’t what it used to be. The danger of the absurd becoming the normal is too great to attempt it.

Case in point. The enlightened leaders of Vancouver’s public schools have, in their new “LGBTTQ+” policy, mandated the use of “gender-free pronouns xe, xem and xyr” (PDF). These replace the usual masculine and feminine pronouns, which, if accidentally heard by (say) a boy pretending to be a girl, might hurt his feelings.

“The Vancouver Board of Education’s policy also includes making restroom and sports activities accessible to all transgender students, regardless of their biological sex.”

How many boys will pretend, at least for the day, to be girls to have access to the girls’ locker room?

Mike Lombardi, vice chairman of the Vancouver Board of Education, said his Humpty-Dumptying of the English language will “create a safe learning environment for every child.”

Don’t giggle, dear reader. Just wait until the school board sends home a form which has been purged of “hurtful” (science- and reality-based) pronouns and which requires you to participate in the Humpty-Dumptying. If you refuse, it will be you who is deemed to be mentally ill, not the fantasists.

Gender no longer means biological sex or grammatical classification of nouns but, “A socially constructed concept of identity based on roles, activities, and appearance such as masculine, feminine, androgynous, etc.”

So if you believe you are a fish, you are a fish. And everybody else ought to believe you’re a fish, too. Who insists you are not a fish is a speciophobe. In this way, socially constructed means self constructed. Reality does not choose your identity, you do. And your choice cannot be questioned. Whatever crime against reality you commit, others must also commit to honor your choice.

This is the way of the malleist. Reality itself must obey our commands.

Fireworks!

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The first one that says “grand finale” gets it. It’s over when it’s over.

I spent a year of boyhood in Chicago, 1975. Actually, Oak Park. An enormous creaky house one block from the Chicago city limits. UFOs were in the air—and on television. There were areas of the house into which I would not go unescorted.

Fireworks were legal. So was the idea that you could set your kids loose in the neighborhood with only the warning “Be home for dinner.”

Who was it that said the past is a foreign country?

We would collect pennies and nickels and trade them for weapons of minimal destruction, or WMDs. We’d take off down the alleys on our bikes lighting bottle rockets from smoldering punks held in our teeth, holding the rockets just until ignition to get a better aim. Not unlike jousting.

My favorites were the plastic green grenades which looked exactly like those my grandpa used to hoist at Germans. Inside was a cardboard tube with a fuse. Tremendous thick clouds of white smoke. But they were expensive. So we’d buy the little round smoke bombs, light two of them and jam them into the grenade. Almost the same effect, but you ran the risk of melting the plastic.

They had this one tiny firecracker the thickness of spaghetti. To show your bravery, you lit one and exploded it in your hand. Some guys pretended to do the same trick with the regular-sized WMDs, but we told each other too many stories of fingers flying in all directions to do it for real. Somebody knew somebody who knew somebody who heard of a guy who lit one he was biting. No takers there.

The elusive goal was a cherry bomb, or M-80, said to be illegal. They were supposed to look like an over-sized smoke bomb and be the equivalent of a quarter stick of dynamite. Rumor always had it the kids in the next neighborhood had one. Massive explosions were attested to. Eyewitness reports were plentiful. But none of us ever had one.

Next best thing was to tape a bunch of regular firecrackers together, twisting their fuses into one. If you did it right, these would go off more or less at once. Looking back, I don’t know how powerful these were. We tried to blow up a bike tire with one. No success.

The same trick, incidentally, can be done with bottle rockets. Tremendous boost in take-off speed. And with snakes, those little cylinders of carbon which when lighted unspool to great length. A pile of five or six would release as much smoke in the air as a press conference by Chuck Schumer.

Remember those little green army men? I had battalions of them. Some came equipped with plastic parachutes, which worked if you were careful about throwing the man in the air just so. Well, all experiments to send a parachuter up with a bottle rocket failed. Oh, he’d soar into the wild blue yonder, all right. Sometimes. But he’d always stick to the stick of the rocket—the parachute would never deploy—or fall off at take off. If anybody ever solved this engineering problem, I’d be glad to hear of it.

Since I am, I blush to say, the Statistician to the Stars, I must present the total of all deaths caused by the WMDs in my neighborhood: 0.

Fingers blown off? 0. Teeth shattered? 0. Eyes poked out? 0. Maimings of any kind? 0.

Burns? Well, one or two, here or there. Mostly from holding the punks or the bottle rockets too long, or just as likely from gripping the match incorrectly or from picking up a thought-to-be-cool spent sparkler. Yes: we used to carry packs of matches everywhere.

But even though no mayhem ensued, it is a logical truism that it could have! And this mere possibly is enough for the more effeminate among us to quail and quake and to invoke the ever-present urge to San Francisco the problem, i.e. to ban, ban, ban. For your own good, naturally.

The “grand finale”, by the way, is the end of the fireworks show, the point where dozens of rockets are sent up at once, an end with a bang. It is the event which is always announced half a dozen times before it really happens.

Happy Fourth of July! But be careful about attending a parade or looking at a flag. You might turn into a Republican.

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