William M. Briggs

Statistician to the Stars!

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Summary Against Modern Thought: God Is Not A Body. Part II

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. All posts are under the category SAMT.

Previous post.

God is not a physical body, that God is not a creature continued…but not finished today. We have instead a series of nested arguments, so it will take some careful reading to keep up. Each argument contains a premise, which is proved in the next point, which itself (once or twice) has a premise proved by the next point after. This goes on at some length; indeed, we will not finish the proof this week. Plus we ranging into analysis-like subjects, which aren’t always easy to keep in mind.

Chapter 20: That God is not a body

9 Again. No infinite power is a power residing in a magnitude. But the power of the first mover is an infinite power. Therefore it does not reside in a magnitude. And thus God, Who is the first mover, is neither a body nor a power residing in a body.i

10 The first proposition is proved as follows. If a power residing in a magnitude be infinite, this magnitude is either finite or infinite. But there is no infinite magnitude, as proved in 3 Phys.[8] and 1 Coeli et Mundi.[9] And it is not possible for a finite magnitude to have an infinite power. Therefore in no magnitude can there be an infinite power.ii

11 That there cannot be an infinite power in a finite magnitude is proved thus. A great power produces in less time an equal effect, which a lesser power produces in more time: of whatever kind this effect may be, whether it be one of alteration, of local movement, or of any other kind of movement. Now an infinite power surpasses every finite power. It follows therefore that it produces its effect more rapidly, by causing a more rapid movement than any finite power. Nor can this greater rapidity be one of time. Therefore it follows that the effect is produced in an indivisible point of time. And thus moving, being moved, and movement will be instantaneous: the contrary of which has been proved in 6 Phys.[10]iii

12 That an infinite power of a finite magnitude cannot cause movement in time, is proved thus. Let A be an infinite power; and AB a part thereof. This part therefore will cause movement in more time. And yet there must be proportion between this time and the time in which the whole power causes movement, since both times are finite. Suppose then these two times to be in proportion as 1 to 10, for it does not affect this argument whether we take this or any other ratio.

Now if we increase the aforesaid finite power, we must decrease the time in proportion to the increase of the power, since a greater power causes movement in less time. If therefore we increase it tenfold, that power will cause movement in a time which will be one-tenth of the time occupied by the first part that we took of the infinite power, namely AB. And yet this power which is ten times the aforesaid power is a finite power, since it has a fixed proportion to a finite power. It follows therefore that a finite power and an infinite power cause movement in an equal time: which is impossible. Therefore an infinite power of a finite magnitude cannot cause movement in any time.iv

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iThis highlights something I think sadly neglected by physicists. That to create something out of nothing, or to be the First Mover (in the Chapter 13 sense; also see this), requires infinite “power.” Just what power and how does that relate to other things we know or conjecture about the universe is very little is known. Infinity is a strange place, as we emphasize repeatedly and to say our intuitions aren’t in it is the minimum. Mathematics barely touches on it. Spheres that can fold themselves inside out without breaking? Can be split in two and be the same in size? Weird!

iiWe’re into the Land of Subtly here, where it is easy to get lost. Don’t forget our destination. That the Infinite cannot be a body. Now if God were an infinite body, that is all there would be. There would be no room for us. God would take up all the space. So God has to be something other than a body, while still being infinite. But what? That’s what the rest of this book of Summa Contra Gentiles is about: describing that what.

It seems to me that we are not at a sticking point, that the reader is willing to grant that God is not an infinite physical body. So I don’t want to take up space with minutiae; nevertheless, if you’re interested in the details, read Chapter 5 of Aristotle here.

iiiNon-locality anyone? How can entangled particles the distance of the universe apart instantaneously “decide” which states to take? Do we have an answer here, in the First Mover, or are things buried more deeply?

ivWe have a proof by contradiction. Perhaps it’s easy to miss, but St Thomas is assuming first that the infinite power causes an effect in finite time. The idea is that, by simple manipulation, if the infinite power causes an effect in any time whatsoever, we can construct a finite power that causes the effect in the same amount of time. This cannot be, thus the infinite power must operate instantaneously.

The proofs of the remaining premises aren’t in this article. We attack these next week because, I think, we’ve already reached the limit today (get it? get it? theological cum mathematical humor; plus, Yours Truly is rather in a hurry today).

[8] Ch. v.
[9] Ch. v. seqq.
[10] Ch. iii.

Scenes From A Mid-Sized University

A feminist riot is an ugly sink, unt, I think that it is just about time dat ve had vone!

A couple of small but notable items, lifted from one issue of a mid-sized university school newspaper.

  • “Student success is a major component of the strategic plan…” Component? Strategic plan? This from an article showing how STEM fields will receive more, and even primary, attention. The strategic plan includes “new Active Learning Classrooms”. As opposed to inactive?
  • “Student Government Associate vice president, [Name] believes if you’re not outraged by what’s going on in the world then you’re not paying attention…’There are so many really intense and scary things going on in America and overseas,’ [Name] said. ‘If we actually empathized those issues, weren’t so separated and actually paid attention to those, we wouldn’t be scared.'”

    So which is it? Outraged or scared? If you’re “outraged”, it’s a good bet you’ve have never read history or a novel which wasn’t chosen by the demographic characteristics of its author.

  • 3,000 is a big number. In an article about September 11, “‘When you hear the number 3,000 it’s a lot, it’s a big number,’ [Name] said. ‘But when you see 3,000 then you realize it’s a big number.'”
  • Headline: “Pizza and networking event aims to end sexual assault.” The hidden power of pepperoni?
  • The above event was sponsored by—can you guess?—the “Women and Gender Studies Program”, the director of which said, “It’s an opportunity to make a collective calendar and learn to be riotous and active and amazing feminists on campus.”
  • A student said about the event, “It’s all about getting people talking and having conscious raising discussions that raise awareness.” I’m confused about what’s being raised, consciouses or awarenesses?
  • In the papers’ op-ed, a student explains her “lifestyle choice”: “For me, eating meat differs from accidentally eating a food I dislike.” It’s the same for me.
  • The rest of the paper, considerably more than half, was given over to the school’s sports teams.

Mark Zuckerberg Dresses Like A Bum

Ugh.

Ugh.

Why I am writing about this, what might seem to you, not-too-pressing subject? The answer is discovered below.

Before the reveal, an example of an ad hominem fallacy: “Facebook is not intelligently run because Mark Zuckerberg is rather plain in the looks department.” It’s the “because” that kills that argument because, of course, the visage of a man has little to do with his intelligence (there is even a slight negative correlation: hello Hollywood!).

An example of true proposition: “Mark Zuckerberg dresses like a negligent college student whose Friday night started late Thursday afternoon (hello CMU!).” Stating true propositions, simple statements of fact, is never a fallacy.

Here’s another: Zuckerberg has seven orders of magnitude more money than I: he rates thirty-some billion, whereas Yours Truly is rapidly approaching (but more usually receding from) multiple triple digits. A point of interest not because it is my duty to provide Facebook free content and Zuckerberg’s to profit from it, but because your author manages to invert the wealth ratio in terms of dress.

Meaning it costs very little to look beautiful. Zuckerberg has much, much more than very little, therefore he can afford to dress beautifully. And it is his duty to do so.

Zuckerberg has so much money that he can pay somebody to buy and take care of his clothes. Zuckerberg himself need never be involved,; he need take no more time than he currently takes in choosing his wardrobe, which is obviously no time at all, except for the microsecond it takes to grab what has fallen on the floor the night before.

One last assertion of fact: this result from a Google image search (one such is found at the top of this post).

Go ahead and try. You’ll see a limited range of images, most containing him in an ugly t-shirt in jeans, but occasionally wearing event-appropriate clothing. Which proves that he knows what it required of him, and sometimes acts on this requirement. But there are several images, such as one at some quasi-governmental official economic forum, in which he should dress nice but is dressed as if suffering from a hangover and has mixed up his wife’s t-shirt with his.

These facts being asserted, it must be that Zuckerberg knows the rules but chooses to flaunt them, knows what it means to dress beautifully but chooses for the most part to be ugly.

So why pick on Zuckerberg?

That’s the wrong question. The better query is: why is Zuckerberg is picking on us?

The man is in the public eye, knows he is, knows we have to look at him, knows that some will emulate him, knows what his duty is but flaunts it, thus he is a major contributor to the degradation of society.

“Briggs, you haven’t been drinking enough. Major contributor to the degradation of society? Time to crack open a bottle, brother. You’ve lost it.”

Major contributor, I say. You’ve heard of the broken windows theory, have you not? How letting little things slide, like graffiti on walls, trash on the lawn, and broken windows encourages far worse crimes like theft, listening to NPR, and voting for Democrats? Indeed, the theory isn’t a theory but common sense put succinctly; isn’t that so?

“Well, yes.”

Same thing here. Zuckerberg’s sloppy t-shirts, jeans, and tennis shoes lead to worse behaviors like instead of looking taking pictures with smart phones wherever one goes, veganism, and public boasting of small “carbon footprints”, not to mention he causes pain every time we have to see him, which, given the media’s obsession with money, is all too often.

But it’s the emulation that is the real curse. The young see a figure in authority clad in dollar-store rejects and figure they can and should do the same. And so whenever we venture outside we all have to pay the price of ugliness surrounding us.

This reminds me: a good statistical project could be to chart the amount of clothing worn by the average individual. Barbarians wore little to nothing; civilization, especially as it probed northwards, led to layering. But increasing decadence is peeling off these layers one by one. If I’m right (and I am), and controlling for weather, most people by 2100 will be down to an extra-large t-shirt, maybe drawers, and flip flops (encrusted with various expensive doodads to signal one’s allegiances).

Update Holy moly! Even the New York Times (sort of): The Death of Adulthood in American Culture (subtract standard self-flagellation about being a white man).

On The Truth And Knowing Why

aard

Guy walks up to you in the street and says, “If f is some continuous function on the closed interval a to b, and if you take the definite integral of that function from a to x, then the first derivative of that definite integral is the function f(x).”

You say, “Sounds spooky to me. How do you know it’s true?”

“It just is, buddy. I don’t know why it’s true, but it is.”

And he’s right. Not just that his statement is true, which it is, but that he doesn’t have to provide you with an explanation why it’s true. That is, his ignorance of the why does not in any way change the truth of the statement.

Now whether this guy, lacking any convincing tale or other corroborative evidence, succeeds in transmitting this truth is another question. But it just doesn’t matter how he came by his truth: whether he proved it from first principles, whether he heard it as a rumor, whether it was revealed to him in a dream, whether he actually thought it was false but was pretending it was true as a little joke, or whether he just insists it is true.

You might be tempted to accept this because you know the example (the readers of this blog are nothing if not mathematically literate); which is to say, you know how to prove the proposition from first principles. But that would be a mistake. The majority of folks who hear propositions like the above will only be able to judge them on the veracity of the deliverer and will not be able to gauge it in any other way.

Think about it. People are asked to believe that (say) neutrinos have mass, and given the source of the pronouncements on this weighty subject, they accept it. Of course, given the lives of most people, this information, like most highly technical and scientific information, is of no use and will not cause anybody to act differently than if they hadn’t believed the proposition.

The weakest argument in favor of something is, as all know, the argument from authority: though despite what you might have heard, it is not a formal fallacy (and most things you believe are probably based on it!). And anyway, even if it were, if any authority were to say, “X is true because I say so”, the statement is no proof of X’s falsity. X can be true even if every argument you know which asserts it is fallacious.

Occasionally we get lucky and are able, from first principles, to formally prove a proposition asserted by an authority false. In the public arena, this is a daily and even trivial occurrence (listen to NPR for dozens of examples of easily disproved propositions). But this is not so in more advanced fields.

You have to work hard, and maybe for years (and maybe never), to identify formal fallacies in the work of many philosophers, and even when you do, you haven’t proven the contentions of these folks false. Proving anything false still requires formal proof. This proof must begin with a list of axioms all agree upon, and lead through successive propositions using rules of argument also believed by all.

In absence of this disproof, it is always the case that the contentions of anybody might be true, even if all that it is offered is an argument from authority (or revelation).

So if somebody on authority contends that an infinite number of turtles supports the earth, you can disbelieve it, but in order to argue its falsity you’re going to need proof. Sneering isn’t proof. Neither is laughter or haughtiness or insults. Nor are other counter-arguments from authority, i.e. “Most philosophers now believe it is aardvarks and not turtles shouldering the burden.”

That one is easy to disprove (an observation will do it). But other contentions are not. And some might even be true, even if you don’t want them to be.

More On Randomness

Anything could be at the end of this lane!

Anything could be at the end of this lane!

I took this picture yesterday (using my mom’s phone: mine can’t offload photos) at the start of the cul de sac, at the bottom of which lies the first job I ever had: washing dishes in a nursing home (in which my uncle now resides).

Who could have guessed I would have moved from there to where I am now?

Certainly not one of my old teachers, who was shocked when told by my parents of my career (such as it is). The teacher was cornered in the back of a grocery store. This same teacher would have taken in stride news that I was just coming up for parole.

This highlights one of the shades of meaning of random. It’s when an event was not just unpredictable, but that it happened almost against the evidence. “That was random,” we say.

This usage acknowledges random is a measure of information, which at least removes some of the mysticism the words has in scientific and mathematical contexts. But maybe not all. We sometimes almost have the idea Nature is working against our desires, though Her actions in this regard are weak.

Mysticism? Did you know that in classic statistical formula if some numbers aren’t imbued—nobody knows how—with randomness, the formula won’t work?

Oh, the formulas will still spit out answers, of course, but you won’t be allowed to use those answers. It’s kind of like sitting down to a feast and discovering the witch doctor didn’t give his prior blessing to the animals cooked, and therefore nobody is allowed to eat.

It’s not just frequentists who believe in magic, but most Bayesians, too. Whenever you hear somebody say, “X is randomly distributed normally” (or some other thing), you have heard an incantation. There is nothing in the world that makes a number “randomly normal” (or whatever). It’s only that our understanding might be quantified by a normal (or whatever).

How X knows it’s supposed to be normal (or whatever) is never specified either. It’s here that the Deadly Sin of Reification mixes with the mysticism of randomness. The formulas become realer than reality, and it’s the power of mysticism which does the deed. But again, nobody knows how. It’s a question which is never asked.

When I’m done with this mini-vacation, I’ll set out more specifically all the shades of meaning of random.

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