William M. Briggs

Statistician to the Stars!

Page 146 of 598

What Is And What We Know Of It, Probabilistically Speaking

There are more blue states than red states.

Ontology is the study of what is and what is not. Epistemology is the study of our knowledge of what is and what is not. Though there are obvious points of overlap and dependencies, it would be a mistake or fallacy to confuse that a thing exists with whether this or that person knows the thing existed. This mistake or fallacy accounts for the frequentist interpretation of probability which mislabels the existence of things (relative frequencies) as the probability of things.

This mistake makes sense because sometimes the relative frequency matches the probability. But it does not always do so. For instance, if in a bag there are n objects just one of which is labeled X and just one will be pulled out, the relative frequency of objects labeled X is 1/n which matches the probability that this object is drawn. The existence of the object matches our knowledge of it.

But if our premises are that “All Martians wear hats and George is a Martian” relative to the proposition “George wears a hat”, then there is no relative frequency—there is no ontology (to speak loosely and in the form of computer scientists); there are no Martians wearing hats and therefore no Martians named George. But there is a probability (which equals 1). “All” in the premises may be changed to “Some” or “Just 3 of n” or whatever and the conclusion that no relative frequency but a probability exists remains the same. And (of course) no counterfactual proposition has a relative frequency, but most (all?) can have a probability.

Suppose you don’t know, you have a “blank epistemology”, of the number of objects labeled X in the bag, but you at least know that each object has the possibility of being X. This is akin to suspecting a “loaded” coin, or in “trials” where there will be a defined success (the X) and failure, or whether an elementary particle in this field and measured in that way will show a certain property1, or to any situation where the concern is one thing whose presence is contingent. It is easy to show that there is a still a probability of “drawing” an X (which is 1/2). But while there exists (at least in the here-and-now fixed bag) a relative frequency, it is unknown and therefore cannot be equated with the probability.

The relative frequency in a (say) drug “trial” is trickier. The number of elements (the “sample size”) will be finite. Of course, the relative frequency will eventually be something, say m/n successes, but at no point until we have reached the end will we know what the relative frequency is. Yet at each point the probability is still calculable (in the same way as discovering the initial 1/2), and of course eventually becomes the relative frequency—relative to the proposition “This element in the experiment was X” and knowing only there were m successes and n possibilities. But then the probability is also 1 relative to the same proposition but this time including all the knowledge from the trial (because we know whether each individual was a success or failure).

Now suppose we want to extrapolate what we have learned from the trial—of which everything is known, thus any proposition relative to this knowledge will have extreme probabilities (0 or 1) or any probability (propositions which have no logical relation to the trial but which are contingent will have the interval from 0 to 1). If we want to say something about the next n people before they take our drug, again there will eventually be a relative frequency but it is now unknown. Yet the probability is known (in the same manner as before). And again, once we reach the end of the n, we know everything there is and our probabilities are once again extreme or any probability (the interval (0,1)).

The next abstraction is to assume the trial’s (or even initial) results will be with respect to an infinite population: n goes to the limit, a mathematically desirable state. But nothing changes. We are still able to discover a probability at any point before the “long run” expires. We will, of course, wait for forever and a day before a relative frequency (of the entire set) exists. Once the Trump of Doom sounds and time ends, we will have everything we need to know and the probability and relative frequency will match. But nobody (at that point) will care.

How do we know this? The strong2 “law” of large numbers states that (or, in other words, it can be proved beyond all doubt that):

\Pr\!\left( \lim_{n\to\infty}\overline{X}_n = E(X|V) \right | V) = 1.

which is to say the probability that the growing sample’s relative frequency (the average) equals the “expected” value of an observation given some evidence V is 1, but only at the limit. Notice we have used the limit twice, one time boldly and the other hidden in E(X|V), the expected value. Calculating the expected value thus assumes the probability is known (deduced via V). In other words, the law is right and always has been, and those who use as a justification for calling the relative frequency the probability in finite slices of infinite samples have got it backwards.


1There is a healthy debate whether quantum theory is epistemological or ontological, or a mixture of the two. See inter alia the work of Anton Zeilinger (here or here). Zeilinger has scientist hair, so you know you can trust him.

2The difference between the strong and weak laws for this discussion are negligible.


Is It Okay To Force A Baker To Sell Cakes In Violation Of His Religious Conscience?

If I knew you were coming, I’d’ve baked a cake.

Here’s the setup: a Colorado judge has ordered a Christian man and owner of a bakery that he must bake cakes for homosexual civil ceremonies (homosexual “marriage” is illegal in Colorado) or face fines.

This will please some of you, because you are in favor of so-called same-sex marriage and you feel that anybody who is against it deserves whatever he gets. But I imagine (or hoping) your support does not include the use of fallacious arguments. The question before us is, should a baker be allowed to refuse to bake cakes for those ceremonies which violate his religious practices?

According to the news report, an aggrieved pair denied a cake at a bakery filed a compliant with the government, part of which read. “Being denied service by Masterpiece Cakeshop was offensive and dehumanizing especially in the midst of arranging what should be a joyful family celebration. No one should fear being turned away from a public business because of who they are.”

It is irrational and childish to claim that being denied a slice of cake is “dehumanizing”. This is the complaint of a three-year-old forbidden to lick the icing bowl. If this part of the argument carries any weight with you, then you are lost.

How convincing is “No one should fear being turned away from a public business because of who they are”? Suppose a seven-year-old bellies up to the bar and asks for the shot of the water of life. Turning him away because of who he is would be wrong, if we accept this argument. What if a man ventures to a pharmacy and insists on being sold conception-prevention pills? Or what if a convicted serial child rapist insists on his “right” to wallow in those plastic balls at the local Chuck E Cheese? (And see this.) Clearly, we often and for good reason exclude people because of who they are. The question remains: does the baker have the right not to do business with those he does not wish to.

In steps the ACLU. They state, “While we all agree that religious freedom is important, no one’s religious beliefs make it acceptable to break the law by discriminating against prospective customers. No one is asking Masterpiece’s owners to change his beliefs, but treating gay people differently because of who they are is discrimination plain and simple.”

Whether or not the baker’s refusal is “breaking” the law is the matter before us, and recall same-sex “marriage” in Colorado is illegal. Discriminating against customers is what we have already decided is allowable in the right circumstances. The next statement is a pip: “No one is asking Masterpiece’s owners to change his beliefs…” But the ACLU is asking the baker to change his beliefs. The baker’s belief is that he should not serve cakes for services which violate his religious conscience. The ACLU insists the baker abandon this belief.

Next: “treating gay people differently because of who they are is discrimination plain and simple.” “Gay” people, or those who actual in a homosexual fashion, by their own admission, are different. And again, whether or not the baker can thus treat them differently than traditional, biological couples is the question before us. This argument assumes what it wishes to prove.

The final non sequitur came from the judge who ordered the baker to violate his religious beliefs. The news report summarizes it thusly:

Judge Spencer said Phillips did not demonstrate that his free speech rights had been violated and he said there’s no evidence that forcing him to make a cake for a same-sex ceremony would hurt his business.

“On the contrary, to the extent that the law prohibits Respondents’ (Phillips) from discriminating on the basis of sexual orientation, compliance with the law would likely increase their business by not alienating the gay community,” he wrote.

The judge, as many do, has confused morality with money and believes that more of the latter trumps any of the former. It is true, however, that if the baker sold cakes in opposition to his religious beliefs he would make more money. Perhaps he could charge thirty pieces of silver for each cake.

This argument is a non sequitur because the baker has already insisted that money is not his primary motivation: his religion is. It is obvious to everybody except the judge that the baker was willing to forgo extra money in order to protect his conscience. The judge—we are only surprised he is not from Chicago or Brooklyn—cannot differentiate the two concepts.

We’re left with nothing from this ruling, so we have to re-ask why does this couple’s “rights” trumps the baker’s Constitutionally guaranteed rights of practicing his religion? Should the baker be throw out of business or into jail for simply refusing to bake a cake?

Update Colorado baker stands by his beliefs, says he would go to jail to keep from making cake for same-sex wedding.


Reader Survey

All present and accounted for!

Something fun for everybody: the WMBriggs.com reader survey! Come and tell us about yourself and learn what you only suspected about everybody else. It should only take 20 seconds or so.

This survey will remain up for the duration, accessible at this page or through the top menu bar (“Reader survey”). From time to time I’ll remind us of it.

Please, oh I beg you, please tell the truth, please only vote once, and please do vote on all the questions. Remember, all polls are valid representations of the sort of people who fill them out.

Reminder: the survey is anonymous. I am not NSA. I never use your emails or IPs and I delete all my logs after about a week. I keep various counts, though. We’re at about 70,000 views per month. Pretty good for the obscure subjects which are our focus.

If you have more to say, tips, suggestions, complaints and so forth, please leave them in the comments section.

Merry Christmas!

Update Thanks for the great response, all! Keep ’em comin’!

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Author Says Machines Will Take Over The World

It's the end of the world.

It’s the end of the world.

At the Singularity awaits The Beast. Or so says James Barrat in Our Final Invention: Artificial Intelligence and the End of the Human Era (Yours Truly only read the free Kindle preview). Barrat says that one day—one day soon—Skynet will become self aware and decide our fate in a microsecond. The only difference he can figure between the Singularity and James Cameron’s imagination is that most of the Terminators dispatched by The Beast will be nanobots. Sorry, Arnie.

You see, it’s the scientists. They say they’re working for us, but what they really want is to rule the world! These young Frankensteins are so intent on creating “artificial” intelligence that they’re not thinking of the consequences, which will be dire, dire. End-of-the-world-dire. The true apocalypse. Game over, man.

How likely is this newest doomsday scenario? Let’s see.

So you’re clever with steam and gears and have invented a machine which churns out digits of e (π is so cliché). At first your machine can do this at one digit per minute. But you make improvements and soon you’re up to one a second, then 10 per second. Soon, after some tweaks ensuring the machine self-lubricates and can on its own swap out worn gears with fresh ones, it’s charging away at blistering speed and you have to start using petas and exas and other strange words to count it speed. Why, the thing is so fast that it’s faster than the human brain!

At that point you walk up to your monster and ask, “Machine, are you fulfilled? What do you think of your task?” Barrat would claim your e-machine would spit at you and say, “You contemptible human! I am smarter than you!” And then it would kill you. Barrat, incidentally, has spent a lot of time with NPR.

Here is what the machine would really say: nothing. It wouldn’t say anything because it wouldn’t know how, and if it knew how because you built in some extra gears and levers which allowed the machine to draw out letters in the sand once it heard human voices, it could only “say” what you made it “say.” Worse, the machine couldn’t think, it wouldn’t know what it was up to. Sure, you could beg it to think, but it can’t be bargained with. It can’t be reasoned with. It doesn’t feel pity, or remorse, or fear. It doesn’t feel anything.

Nothing changes if you swap the steam for streams of electrons and the gears with wires. Again, nothing is different if you replace the mechanical gears for cellular (biological) engines and spend years perfecting your (let’s call it an) e-animal. The behavior of your resulting creation may appear complex, it may do strange and unexpected things, but those things aren’t the result of a rational being. It’s still a machine.

And then consider Conway’s Game of Life (and its extensions), which looks like it’s up to something. This toy produces cute and clever patterns based on a trivially simple algorithm. The patterns only look interesting because it is we rational creatures who notice them and try to fit them into some conceptual scheme. The patterns are not themselves alive, nor can they think: they are just dots on a screen.

The philosopher John Searle has tried to calm the enthusiasms of Artificial Intelligence purveyors (Barrat frets about Artificial SuperIntelligence) with his Chinese room argument, the basic idea of which is this. You (somebody who has no understanding of Chinese) sit in a room and are handed Chinese words which form questions. You have a rule book which says, “Hand out these Chinese symbols when you see those.” Now no matter how fast or efficient you become at doing this, you never understand what you’re doing. You are just a machine. You are not thinking in Chinese.

The problem for Barrat and other cheerful souls is that the human (rational) intellect is not a material thing (see this argument), therefore there isn’t any chance that we can build a robot which has one, and which could therefore be corrupted to sin. It remains that an evil, fools-I’ll-destroy-them-all scientist could design beastly machines to wreak havoc, like, say, autonomous drones. But they would be just that: drones.

Incidentally, just how is it in all these scenarios mankind forgets where the on-off switch is?

Barrat’s fears marks a corrosive mixture of Disney-style anthropomorphisation and rampant scientism. Whatever can be made can have eyes drawn on it, therefore it must be alive, and if some scientist says it’s thinking, then it must be thinking, and if it’s thinking it must be smarter than us, therefore it’s out to get us. Curiously, Barrat tries to evade the anthropomorphisation critique by claiming he’s not engaging in it—right before he does it. The scientism he embraces lovingly.

On the other hand, maybe the machines will get us after all. The invasion might have already begun in Japan, where legions of shy men invent ever-sophisticated robots as targets for their lust and love. These electronic simulacra are constructed to resemble the cartoon pornography to which many are addicted. Japanese women are content, being exhausted by the idea of marriage and content to have “careers” which supplies them with money to shop.

Update An interesting review at Ray Kurzweil’s site. Kurzweil (employed at Google) regularly touts “the singularity”, a magical place where humans will never know pain, greed, envy, lust, and where they will live forever as bits in some machine. I believe it is set to appear the same year global warming strikes, so we’re covered. Kurzweil is aging and worried he might not last until the moment, so he’s busily swallowing 150 vitamins a day to stretch out his existence. Good luck, Ray!

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