That fundamental problem [with the Torino and Palermo impact risk scales] is that in any information system in which a function yields a single scalar value to represent more
than one dimension of argument, it is a good bet that that function will be a source
of trouble. This is a venerable principle in data base theory and a commonplace in
data base practice.... Furthermore, if the function is not monotonic, so that a higher
value of function need not represent a higher level of concern, that is the goat pill
on the top. In the example of the Torino scale, higher values of function do not map
onto say higher levels of hazard or of risk, or at least of newsworthiness, and
tinkering with the function will not solve the problem.
    --Jon Richfield, CCNet, 20 October 2003

By Jon Richfield <>

Approaches to avoiding conflation
Discarding risk scales
Vector encapsulation of risk dimensions
Urgency (immanence)

1. Introduction

Some years ago I proposed a scheme for the categorisation of NEO threats (It might still be somewhere in the CCNet archives, but I have lost my original). At the time it met with little enthusiasm because correspondents considered it too complex for the public to understand. I had my doubts, but uncharacteristically held my peace. Since then however, several scares have led to dramatic storms in publicity teacups, and I though my proposal could not have prevented all the problems we have seen, I suggest that it could have reduced the mess.

Many of the complainants are pointing at the Torino scale, and to a degree rightly so, but few seem to have identified the key reasons for the problems. The first and worst was implicit in the design of such scales and I was surprised that no one pointed out the flaw on day one; it is an obvious and basic blunder in data design. What is worse, the same weakness would apply to the Palermo scale if it were used in the same way as the Torino scale. The Palermo scale is more sophisticated and has different design objectives, but its main saving grace from the publicity point of view is that it is too unintelligible for tempt most of the least responsible journalists to abuse it.


That fundamental problem I mentioned is that in any information system in which a function yields a single scalar value to represent more than one dimension of argument, it is a good bet that that function will be a source of trouble. This is a venerable principle in data base theory and a commonplace in data base practice. If the scalar is a function of independent arguments, the argument values cannot be deduced uniquely from the function value unless it can be shown that the arguments are in combination relevant but individually irrelevant. This is hard to imagine if the arguments really are mutually independent.

Furthermore, if the function is not monotonic, so that a higher value of function need not represent a higher level of concern, that is the goat pill on the top. In the example of the Torino scale, higher values of function do not map onto say higher levels of hazard or of risk, or at least of newsworthiness, and tinkering with the function will not solve the problem.

Consider the contrasting example of earthquakes. A scale such as Richter represents in essence just the dimension of energy as measured by particular types of seismograph. One might argue about how useful that function is, but at least no one is left in doubt about what it means, and the worst confusion one sees in the press is that reporters often seem to think that say a magnitude 3 is half as bad as a magnitude 6.

So far so good, but to the public there are more relevant parameters to an NEO than to a quake. For one thing, we seldom know much about a quake till after it has struck. There is little question of how to prevent it (I have my ideas, but those do not matter here!) Therefore there is no question of the scale having to represent dimensions of probability or urgency. In contrast an NEO might be contemplated, measured and discussed in increasing detail for years in advance of any possible impact, and there are whole classes of conceivable preventive measures.

Now the Torino scale would have been fine if all it represented was say, the product of mass and the square of speed relative to Earth, as reflecting probable destructiveness or something of that sort, but of course such a function is seldom relevant in practice; it would put say Halley's comet or Mercury pretty high on the scale although neither is a material threat at present. The designers of the scale obviously tried to create a function that usefully indicates a threshold of threat beyond which one should, or should not be concerned for the sake of humanity. The trouble is that the scale they produced amounts to a table with coordinates of two dimensions but unfolded into a linear scale. Those coordinates are magnitude and probability or closeness of encounter (perhaps with a vague implication of relative urgency).

Unfortunately, for such an application a scalar value in a linear scale suggests, if it does not actually imply, that a value of three is similar in kind, if not in magnitude, to a value of say, seven. This is not the case with the Torino scale. Comparing values on the Torino scale is rather like arguing whether the square root of minus nine is larger or smaller than three. If you do not take care you find yourself not so much wrong, as talking nonsense. What is worse in this case, if you are talking to a layman in the subject you find yourself unable to convey anything but nonsense, no matter how sound all your statements might be.

You think I am being unreasonable? Then inspect the recent history of reports in the world news media. Consider their sense, relevance to the respective threats, and impact on our planetary readiness to deal with future threats.

I think I might comfortably rest my case concerning that point.

As for the Palermo scale, it is just as well that it was never intended as a notation for lay public information. It was designed for the use of professionals, who presumably understand its limitations and utility. Its lack of obvious relevance to anything that the public might want to know about any single forecast event would make it a dangerous toy in the hands of journalists.

Risk functions such as the Palermo scale are of most use to actuaries, epidemiologists and others who deal in collective risks rather than characterising particular potential events. For instance, for such purposes it would make very doubtful sense to rank scalar values representing large hazards of low probability on the same scale as small hazards of high probability. Practical decision analysis could make little use of such figures as a primary resource in dealing with a specific event, let alone base action on them. While the function is mapped by the coordinates, the coordinates are not mapped by the function. And in such an individual case the coordinates matter.

I re-emphasise that this is not a criticism of the Palermo scale in absolute terms, but it remains at best irrelevant to the subject of lay public information.

So much for the fact that we do not at the time of writing have an adequate snapshot function to keep the public and the news media responsibly alerted and appropriately informed of the status of a detected risk. As I see it there are two things that could (or should?) be done. I do not for an instant suspect that any one system will cover all problems, but after all that is just the way reality works. Insisting on doing something inappropriate to satisfy unreasonable demands just because no appropriate measure exists, is to exacerbate the problem and invite disaster, political and otherwise for the sake of immediate political convenience.

I do not deny the importance of political convenience, but it should by now have become plain that the long-term cost of quickly satisfying the press can be unacceptably high.

Even in politics.

Approaches to avoiding conflation

Discarding risk scales

The simplest approach is to discard the risk scales entirely.

All the valid functions of such scales could be supplied by continuing to maintain Internet tables such as the one on the JPL Sentry System site, possibly with expanded explanations and legend, but without the Torino column. Permit entries such as "?" or "large, still being measured" for doubtful values. Include a prominent disclaimer at the head and foot of the table explaining that the information is all tentative and constantly under correction, and leave it at that.

It also might be preferable to include a parameter indicating the radial uncertainty of the closest approach to Earth, instead of a figure for probability of impact. Then instead of trying to explain to innumerate reporters what the significance of an impact probability of 9.7e-05 might be, they would see that the best current guess is to pass say within 200000 km of Earth, with a possible error of 210000 km. The reporter could then decide for himself whether to be alarmed or not, but could not blame whatever he then disseminated on what some astronomical spokesman had told him.

Also, at least one table should include, instead of the cumulative probability and number of approaches, the date and expected closeness of each approach.

First of all, such tables would be adequate defence against charges of irresponsible secrecy. They would be quite adequate for reasonably well informed laymen, while the fact that it would take a little literacy, numeracy, digging, and good sense to use them, would discourage most of the real idiots from consulting them.

No Torino-style function need be published at all. Any responsible journalist should be able to see what she or he needs to know, almost at a glance after having checked what the columns mean. That might seem too demanding for the typical journalist, but it is far less demanding than making sense of the meaning of a scalar function in such a context.

Vector encapsulation of risk dimensions

If anyone really feels that we must, must, really, really must have a function that encapsulates the risk, then so be it, but any function that conflates its independent arguments is unconditionally unacceptable. It is no good arguing that idiots among the press and the public cannot understand more than one number at a time; no one, no matter how well educated, can really understand just one number at a time if it represents multiple independent dimensions. With the loss of each dimension there is a loss of information, in this case relevant information. If someone insists on what amounts to a summary of the importance of a particular observation on a particular NEO, then it is no good giving him an oversimplification if that oversimplification is wrong. It is no good pleading that he insisted on the oversimplification. You may reap the wind if you refuse to supply the oversimplification, but will certainly reap the whirlwind if you do supply it.

So far the fuss and bother we have seen has been the mildest of zephyrs compared to the whirlwind that will inevitably strike sooner or later if we do not avoid supplying information so prone to misleading journalistic abuse.

And tinkering with the Torino scale, as I said earlier, will change nothing of importance.

Well then, if a single scalar cannot meet the case, then what vector might be useful, short of a table? The salient parameters as I see them are magnitude (absolute hazard), (absolute) probability of impact, and estimated urgency of dealing with the threat. There are a lot of approaches to constructing such a scale, but let us consider a illustrative first attempt.

Assign a single-digit value to each of those three parameters, allowing certain letters to code for uncertainty too great for useful quantification. Each digit would range from 0 to 9, where 0 is the smallest value and 9 the largest. This notation divides each dimension into ten intervals whether that is necessary or not.

The letters could be say: N for never or not applicable, P for positive, as in an effectively certain event, U for unknown, and X for omission of a parameter for the sake of generalisation. The third column could also be omitted instead of getting an X, and if only one column is given, that is equivalent to omitting Xs in the last two columns.

It might seem more difficult for a reporter to deal with a vector like 713 or 255 rather than a scalar Torino value of 2, but I trust that I have by now justified my claim that the relative simplicity of the single digit is an illusion.

Of course the whole scheme as I present it could benefit from a lot of editing and rationalisation. It is just a first sketch, but something of the type should satisfy the press.


For the first digit of the code I propose a logarithmic function of the estimated destructive power of the impact, should it occur. Exactly how to scale it would be subject to some tuning, but bearing in mind what the press would want to know, something of this type should be desirable:

Less than a ton of TNT equivalent. Dog killer to house buster.
Tons. Blockbuster
Kilotons. Town buster
Megatons. City buster.
Region wiper.
Country leveller.
Continent wiper,
Hemisphere wiper.
Dino killer
Planet buster
U. Unknown, presumed large

X. The size is not under discussion.


The next digit could be calculated as the log of the probability of impact expressed in parts per billion, or less. So, if the probability were less than or equal to 1e-9, the digit would read 0. If it were 7e-7, the digit would read 2 and so on. Whether to round off or to round up or down, I leave open to debate.

Exactly how competent astronomers and statisticians would calculate the raw probability of impact, I do not propose to suggest.

The table of significance for the probability of the event could be something like:

Less than one in a billion probability of impact during any reasonable time period.
Less than ten in a billion, something like winning a really large lottery that you really want to lose.
Less than one in ten million

Somewhere between one in ten and dead certain. Time to run in circles, scream and shout.
N. Never. Could not under any reasonable assumptions pose a threat.

P. Positive. There is no reasonable doubt that there will be an impact. Relax or not, as preferred.

U. Unknown, not yet clearly a serious concern, but watch this space

X Probability not under discussion.

Urgency (immanence)

The urgency digit is open to debate, because it could most simply express the estimated time to impact, but one might prefer to express it as the ratio of time required to prevent disaster, to time available. As no one has yet proposed definite countermeasures, I propose that for the time being we just make it an inverse function of the time remaining before the moment of maximal threat. For this a decimal digit is over generous, but we could do something like:

Millennia, but not excluded forever, as opposed to code N.
Centuries (not an academic point; it might take that long to deflect a big one!)
several hours
one hour
N. Never -- an indefinite period or vanishingly improbable

U. Unknown

X. Urgency not under discussion.

This could be tidied up a little, but as it stands it is not unreasonable. A millennium is about 1e10.5 seconds, and in nine logarithmic steps we get down to the order of 1e1.5 seconds.

Presumably codes 7 to 9 would be academic under normal circumstances.


As an illustrative thumbsuck, 2003 QO104 might have been given a code of 431. We could class its magnitude as Region wiper. The early probability of collision was better than one in one million, and it will be decades before the point of maximum threat.

Usually the first entry for a particular NEO might be UUU, possibly followed by say, 3U2, 312, then 3NN or the like.

Too obscure? Maybe, but mild obscurity should be a good repellent for the idiots among the reporters. It still would make a lot more sense than a 1 on the Torino scale, and more useful to the press than -1.66 on the Palermo, if only because it at least _answers_ the questions it is meant to answer, and does so specifically and explicitly.

For one thing, the significance of the range of digits possible in each position is monotonic and logarithmic.

Nor is a three digit number a major challenge to remember; it is a lot simpler than the 1-digit Torino, where one must mentally convert the one-dimensional number to a 3X3 array of sparse information.

So, why not? Either just tabular data or a compact three-digit code.

Jon Richfield

It is impossible for a man to learn what he thinks he already knows.

CCCMENU CCC for 2003