William M. Briggs

Statistician to the Stars!

Page 148 of 597

What Random Means In Random Number Generation

Dice throws appear random because their outcomes cannot be predicted naively. But knowing the physics and initial conditions, they can be predicted, and so are not truly random.

Thinking about one-time pads reminded me to point this out.

It’s simple, really. A “random” number generator spits out a string of numbers or characters from some set, say c1, c2,…, cp, where each of these is a character out of p total. Example: c1 = ‘a’, c2 = ‘b’, etc.

Before the generator starts, using only the premises that the generator can produce only these p characters, we deduce the probability that the first character is ci (for any i in 1 to p) as 1/p.

Start the generator. The characters roll out one at a time. To be be considered “random”, this condition must hold:

     Pr( Ct = ci | C1, C2, Ct-1, generator premises) = 1/p for all t and all i,

where I mean by this notation that the probability the next character (Ct) will be one of the set is 1/p no matter how far along in the series we are (short of infinity) and no matter what character we consider. The “generator premises” are those which state only the characters c1 through cp are available, etc.

In other words, if there is any information in the series to date that allows us to calculate any probability other than 1/p for Ct, then the series is not “random.” Be clear that “allows us” means “logically possible” and not necessarily practical or in-practice possible. There may be some existence proof which says something like “Given this generator and an output series like this-and-such, the probability of Ct is x, which does not equal 1/p”. We may never see the this-and-such series, but still if the output series is possible, then the output is not “random.”

Now don’t start going all frequentist on me and say, “Look here, Briggs, you fool. I’ve ran the generator a finite number of times and the relative frequencies of the observed Ct don’t match 1/p.” I’d reply, “Get back to me when you reach an infinite number of times.”

Run the generator for just one character. The observed relative frequencies will be 0, 0, …, 1, …, 0, where it’s 0s for all ci except the 1 character which showed. What does this prove? Next to nothing. Probability just isn’t relative frequency, but relative frequency can match the probability. Probabilities predict relative frequencies. In that spirit, we know the series is not “random” if we can do a better job predicting the series than saying the probability of the next character is 1/p (for any character).

But I see the idea of relative frequency is still alluring. Perhaps this is why. There is in math the idea of a “normal” number, unfortunately named because “normal” in probability means something else. A normal string or number is one in which the digits/characters repeat equally often, yea even unto infinity. Examples: 0.111222333444555666777888999000111222… and ‘abcabcabcabc…’ (we know the numbers are limited to digits 0-9, but here I limit the characters to a,b,c).

These normal numbers are in no sense “random”, because if you know where you are you know with certainty what the next digit or character is. Plus, there are some technical ideas, where a number may be normal in one base (say 10 or 2) but not normal in another base. Here is an example of a number, Stoneham’s constant, which is normal in one base but not another. So “normal” does not imply random, but we have the sense that “random” implies “normal”, which it does.

Truly “random” numbers are probably (I don’t believe there is a proof) normal in any base. Another way to put it, in terms on information, is to say that the number cannot be compressed (in any base); that is, speaking loosely, that it takes just as many characters to compress the number as to display it. The above-linked article gives some hints on the “randomness” of π, which appears normal in many (all?) bases and which cannot be compressed. So where do the digits of π and other transcendental numbers come from? Only God knows.

Last point: many “random” number generators—where by now we see that “random” merely means unknown or unpredictable in some sense—are wholly predictable, they are fully deterministic. Start at a known output and the path can be predicted with certainty. These are called “pseudo-random” generators because the numbers only appear unpredictable.

And what does that mean? Appear unpredictable? Well, it means not-random, that we can prove that a set of premises exist which predict the series perfectly. The difference between a “random” generator is that we can prove no such set of premises exist.


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Winner Announced in What Do You Call A Believer In Scientism Contest

At least they’ll subsidize your cane.

Last week we asked what is the best word or term for a die-hard believer in scientism? The response was overwhelming!

More than 50 people entered some 100 words. I grouped these into three-plus-one categories: Honorable Mentions, Runner Ups, and Top 10. But there can be only one! Winner, that is, who will receive a Kindle copy of Iain Murray’s not-to-be-missed Stealing You Blind.

All complaints or suggestions about the entries, rules, or my judging may be entered at this site.

Special Mention

Thinkologist (davebowne).

Love it, but I was saving this for a special use on certified Experts. So it was not in the running for the contest.

Honorable Mentions

In no particular order:

Evidencist (Francsois). Inscienaty, Narrow-Minder, Rationer, Reasoner, Sciencerapist (Pedro Erik). Science Zombie (JohnK; Davebowne). Bright (Thinkling; Mariner). Supercilioust (HowardW). Scimoron (GaryL). Positivist (Philip Neal). Psysciphilliac (BradH). Sheldonists, Optimists, Triverist (Paul Murphy). Knowlatan, Pedantocrat, Patronisiac (Hamish McCallum). Unscientific Hucksterists, Philistine Scientists, Scientific Excrescence, Vulgar Scientists (Jim Fedako). Scatomancer, Weepees (Bruce Foutch). Scisyphist, Scisyphean (Jonathan S). Scienterrific (An Engineer). Scienzealot (Charles Boncelet), Scientomancer (hmi). Anthropodogmatists (Pangloss). Scinsist (Jeffrey).

Runner Ups

In no particular order:

Scientite (Adrian Hilton). Fatuotist (as in “fatuous”; Bob Mrotek). Scientizer, Scientaster, Scifollogist, Sciphist (Jester). Spockists (Toby Young). Scientician (TheRealAaron). Sciencista (Mike Anderson). Scientocracy (K). Sciphist (John Baglien). Technogogue, Techogogue, Scientologue (Mark Webster). Scientificant, Saintificist, Saintologist, Scientificist (Bob). Aoristicist (Don Jackson). Scienticist (Edmund Kartoffel; David). Scientipher, Scientifie (Mike B). Scientient (Andy). Scientismion, Scientismidel, (Aloysius Hogan, who had 42 generated entries, such as Scientismafuego derived from Cacafuego, a ship all fans of Patrick O’Brian will recognize; only the top are shown).

Top 10

In winning order:

  1. Scientificalist (Ye Olde Statisician)
  2. Obfuscator Scienista (Bruce Foutch)
  3. Scientismist (Adrian Hilton)
  4. Sciphiliac (Rich)
  5. Scientophile (Andy)
  6. Scientiscubus (Aloysius Hogan)
  7. Sighintists (John M)
  8. Scientocrat (K)
  9. Academagogue (Mark Webster)

Winner

Scidolator from Mason Kinney. This portmanteau was the truest and most evocative entry. It tells you what it is without having to explain it; it is memorable, it is short and easy to say. It can be spelled. It captures beautifully the spirit of over-dependence on science. It cannot be improved upon.

Why does 1 + 1 = 2? Science doesn’t know. Why is murder wrong? Science can’t tell us. Why are the fundamental laws of the universe what they are? Science is silent. Why is there something rather than nothing? Science is of no help. Why is killing an unborn child immoral? Science has nothing to say. Why is it that if All F are G and x is an F that x is G? Science is dumbfounded. What is good and what bad? Science says, “You talkin’ to me?” How can free will exist in a deterministic universe? Science hasn’t a clue.

It is not only that Science cannot answer these questions now, but that it never can. All these and many more are forever beyond the reach of empiricism. There is no observation in the universe, nor can there be, nor will there ever be, which proves e^{i\pi} = -1. It is impossible to peer at the Unmoved Mover, yet He must be there or, quite literally, nothing would happen.

A scidolator disagrees, but because of the impossibility of the acts just mentioned, he quickly changes the subject. Scientism is thus a dread and growing disease and a word which identifies its holders and devotees while simultaneously highlighting the malady from which they suffer was badly needed. Scidolator is that word.

Thanks to all for participating!


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A Survey Of The Perceptions Of Climate Scientists 2013: No Consensus

Nothing like a balmy summer afternoon.

Earlier this year scientists were given a survey on their opinion of the state of climate science. This was administered by Dennis Bray & Hans von Storch at the Helmholtz Zentrum Geesthacht. (Bray I don’t know, but von Storch I do, vaguely).

The paper is on-line here (free registration required). Update Alternate link at Bray’s site (near the top).

The authors started with 5,947 (reasonably discovered, mostly senior folks from USA, Germany, and UK) email addresses (culled from earlier surveys), but had to toss 1,456 for invalidity. Only 286 people turned in a survey. I was one. This makes for a very dismal 7% response rate. Any conclusions drawn from this study should therefore be viewed with fish eyes, because 93% had noting to say, did not to participate, who knows why.

What follows is a summary. Most questions were on a 7-point scale, higher more confident, increased significantly, that sort of thing. I dichotomize these, with 4 (neutral) and above or 3 and lower.

Main: No Consensus

Only 8% (of the 7%) said their “confidence in the findings of climate science” decreased. Which is to say—and not for the last time—there is no consensus. Of the other 93% who didn’t turn in a survey, nobody knows. But there are at least some who aren’t so happy with the state of affairs in climatology (I’m one).

On a bright note (to me), about 36% did not agree that “climate science has remained a value-neutral science.” But no consensus.

Around 11% felt “less confident concerning the IPCC’s attribution of warming to GHS”. No consensus in the 7%.

Model Modules: No Consensus

Some 20% did not agree that “Climate models accurately simulate the climatic conditions for which they are calibrated.” No C. Same number of folks disagreed that atmospheric models deal well with hydrodynamics. Only 10% were skeptical of modeling radiation. But 26% worried about simulate vapour in the atmosphere.

And a whole 60% admitted that climate models don’t do well with “the influence of clouds.” About half had the same negative view of precipitation, and between 50-60% frowned on atmospheric convection. Gee, No C.

The same pattern repeated itself for ocean modeling, so I won’t repeat it, except to note that 24% did not think models had the “ability to couple atmospheric and ocean models.” No C again.

What about turbulence in climate models? Just under half said no confidence; 28% said nope to land surface processes; about the same were dim on sea ice. Least negative were views on surface albedo and “green house gases emitted from anthropogenic sources”; about 14% were negative on each. No C.

Model Mimicking: No Consensus

About 9% were skeptical that models were able to reproduce both “mean values for the last 50 years” and “trends for the last 50 years”. More than double that (around 21%) were skeptical about reproducing “variability for the last 50 years.” Some 24% didn’t think models did well with precipitation over the last 50 years.

Even more—37%—said the models could not reproduce “trends for the last 50 years.” And even more still (52%!) thought models blew it on “variability for the last 50 years”. Talk about no consensus! (Of the 7%.)

Model Predictions: No Consensus

Despite that half thought models stank at reproducing variability, only 25% (why not the same 50%?) or so thought models would not well predict “mean values for the next 10 years” nor would they well predict “trends for the next 10 years.” And even more, around 38%, didn’t think models will do well with “variability for the next 10 years.” No C again.

It was the same story for predicting 50 years ahead, with even more folks skeptical of models making such long-range predictions.

Predicted precipitation? 42% said no to “mean values for the next 10 years”; 54% or so said no to “trends for the next 10 years”; and around 68% said no to “variability for the next 10 years.” Out 50 years, and skepticism only grows (as it should). No C.

Sea-level rise? Around 19% said no to good predictions of “mean values for the next 10 years”. About 23% said no to “trends for the next 10 years”, and about 31% said no to “variability for the next 10 years.” As before, out 50 years and only a handful believe. No C.

Extreme events? Over half (52%) didn’t think models would do well predicting “mean values for the next 10 years.” Around 60% said no to “trends for the next 10 years” and some 66% said no to “variability for the next 10 years.” Once more, looking out 50 years produces very little confidence. No C.

The authors also asked a series of questions on regional models, which produced less agreement than the global models; indeed, the majority were skeptical on many questions. No Consensus discovered. (Of the few who bothered to answer.)

Impact!: No Consensus

Around 28% didn’t think they had much to say about “the detrimental effects that climate change will have on society”.

Pay attention: The closest to a Consensus was to the question “How convinced are you that climate change, whether natural or anthropogenic, is occurring now?” Only 2% disagreed. Now, if even this banal, harmless question (“natural or anthropogenic“) cannot produce a Consensus, then what can?

About 11% were not convinced “that most of recent or near future climate change is, or will be, a result of anthropogenic causes”; about 14% were not convinced “that climate change poses a very serious and dangerous threat to humanity”. Note the words very serious.

Some 9% didn’t think we were feeling effects of a changed climate yet. But 38% said we could not “ttribute recent climate related disasters to climate change (anthropogenic or otherwise)”. Note that “anthropogenic or otherwise”.

The hardest question to summarize was this: “Since 1850, it is estimated that the world has warmed by 0.7 degrees C. Approximately what percent would you attribute to human causes?” About 10% said thirty-percent attribution or less. The peak was 26% at eighty-percent attribution. But, no consensus.

View: No Consensus

There then followed a series of questions on what interactions climate scientists had with the public. But about 60% of scientists said that adaptation is better than mitigation when dealing with climate change problems. Whoa!

Again, around 60% disagreed with the practice which some scientists employ; those who “present extreme accounts of catastrophic impacts related to climate change in a popular format with the claim that it is their task to alert the public.” (Bad news, right, Gav?) But still no consensus.

Even 33% said it was not the job of climate scientists to “be directly involved in alerting the general public about the possible socio-economic consequences to humans (health, policies, damages, economic loss, etc.) resulting from changes in the climate”

There then followed a few more questions along the same lines, all pointing to mixed views on the proper role of scientists and public policy.

Indulge Me: You can skip this section

The last few questions were of interest to statisticians. To “A description of the most probable outcome best defines” 28% said “a projection”, 64% said “a prediction”, and the rest “other.”

To “A description of a possible outcome best defines” 62% said “a projection”, 16% said “a prediction”, and the rest “other.”

To “From a scenario simulation prepared with climate models, scientists are more inclined to make” 76% said “a projection” and 18% “a prediction” and the rest “other.”

Now, since according to logic, all predictions are conditional (as all probability is condition), there is no difference in “a projection” or “a prediction.” Though I have the idea more people would like to hide behind the former, as it sounds weaker. More on this another day.

Overall Conclusion

I’m struggling to tie a theme together. Maybe readers can help me?



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North Korea’s Brilliant Climate Change Strategy

Originally seen on Real Science, and culled from the US Department of Energy (thank you, Government!), comes this informative picture:

North Korea leads the world in reductions.

North Korea leads the world in reductions.

Environmental activists are surely taking notes on the Democratic People’s Republic of Korea. They’re paying special attention to that master climatologist and man of the People Kim Jong-il, who assumed power, to unanimous assent—if only our Congress were as efficient!—from his pappy Kim Il-sung in 1994.

Yes, it is no coincidence that the rates of carbon usage began to plummet as Jong-jong (as he was affectionately known) ascended to the throne.

Activists credit Jong-jong’s astonishing success to that Supreme Leader’s invention of the simple “carbon lock box.” This was an ordinary box, about 1.5 meters long, and about 0.5 half meters wide and high, constructed of renewable and sustainable resources (pine planks).

This alone was brilliant, but it his next move that turned his idea into genius. Jong-jong dispatched an army of environmental agents to solicit resident of the People’s paradise to volunteer to “do their part” in the great battle against global warming. These altruistic folks—and there were many, many—literally stored away their carbon in lock boxes, forever depriving it to the atmosphere. Amazing!

That graph illustrates the kind of change we can believe it. It shows you what Government can do when gridlock is removed, when leaders are no longer restrained by pettifogging, obstructionist opposition. No filibustering in North Korean. No, sir! If only we could have the same kind of enlightened rule here.

Perhaps Kim Jong-un, the son of Jong-jong and new Supreme Leader of the People, would consent to loan us one of his issue, say his second or third born? Of course, we may have to wait a while for this gift. Jong-un had his last girlfriend machine gunned to several thousand pieces. But she had it coming.


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