A Scientific Critique of the Accident Risks from the Cassini Space Mission

By: Dr. Michio Kaku

Henry Semat Professor of Theoretical Physics
Physics Department
City University of New York
New York NY 10031

Note: This article is also available in a german translation courtesy of the Netzwerk Friedenskooperative (Network of the German Peace Movement).

Abstract: If we carefully re-examine, line-by-line, the physics analysis behind NASA's Final Environmental Impact Statement, we find that the FEIS has consistently underestimated the possible risks of an accident with the Cassini space mission. Originally, NASA estimated the number of cancer fatalities from a maximum credible accident over a 50 year period to be 2,300. We detail how this figure of 2,300 deaths could easily be off by a factor of 100, i.e. true casualty figures for a maximum accident might number over 200,000. Furthermore, property damage and lawsuits could be in the tens of billions. In addition, the FEIS has over- estimated the difficulty of using alternate sources of energy, such as solar and fuel cells. In line with the new NASA philosophy of faster, cheaper, better, the Cassini mission should be downsized and made into smaller, more frequent solar-powered missions to Saturn with less power requirements.

I. Introduction

The Cassini mission contains about 400,000 curies of plutonium-238, making it the largest space mission ever undertaken involving plutonium power packs (RTGs). The plutonium, about 72 pounds in weight, is distributed in 3 RTGs, with 18 modules each. If that quantity of plutonium is somehow dispersed into a populated environment, there is no question that such an accident could cause significant health effects resulting in thousands of casualties. All scientific experts are agreed on this point.

What divides the experts is:

(a) how much plutonium can be realistically released in a maximum credible accident and
(b) the likelihood of such an event.

All parties are agreed that such an event is unlikely. It may happen that the Cassini mission may be a resounding, flawless success. However, it's only a matter of time before some disaster strikes. Instead of relying on misleading computer programs which tell you what you want to hear, one should carefully examine the actual track record of accidents in the space program, with numerous booster rocket failures and space probes which malfunction.

Unfortunately, the true risks from such an accident and the consequences have been downplayed. In a democracy, the American people can make rational decisions only on the basis of scientific truth, not simplistic, misleading press releases. It is inevitable that there will be spectacular accidents with the space program, some involving casualties, and the American people have a democratic right to know what the true risks are. Thus, it is a matter of scientific interest to go over line-by-line the calculation of the FEIS.

NASA calculates in its FEIS that up to 2,300 people might come down with fatal cancer over a 50 year period from the dispersal of plutonium-238 over a populated area. More recently, it has lowered this figure to 120. However, the calculation of these figures depends on three important steps, each of which has been underestimated by NASA:

the calculation of the "source term," i.e. the amount of plutonium-238 which actually escapes and is dispersed into the environment
the calculation of the land contamination area over which the plutonium-238 is spread
the calculation of the population density and how many may come down with cancer.

In each category, we will show that:

a) the FEIS consistently underestimates the possible risks, avoiding the maximum credible scenarios.
b) since NASA has never conducted a full-scale test of a realistic accident scenario, the FEIS simply makes up numbers to compensate for its ignorance. However, the FEIS consistently fabricates these numbers in a certain way: to arrive at the lowest casualty figures.
c) the FEIS disguises this fact by giving the results to three significant figures, which makes the figures seem authoritative and accurate, when in fact they are largely created by fiction. Of course, it is justified to make estimates. But it is then standard procedure within the scientific community to give error bars or estimates of uncertainty. However, one immediately spots a glaring error: no uncertainties are ever given in the FEIS, which is a serious flaw. No uncertainties are given because their numbers are simple educated guesses, not real experimental numbers at all.

II. Calculation of Casualties from a Maximum Accident

A Launch Phase (Phase 1,5 and 6)

We will investigate all three steps for two crucial phases, the early launch phase and the fly-by phase.

a) Source Term
The most important component of the calculation is the determination of the "source term." The FEIS admits that plutonium will escape from the RTGs during an accident both in the launch phase as well as the fly-by. However, the FEIS typically concedes that only a tiny fraction of a percent of the plutonium inventory will escape. This severely underestimates the true impact of a maximum credible accident and results in artificially low casualty figures. This is the main weakness of the FEIS.
The FEIS admits that plutonium in the RTGs will be subject to three extreme conditions during a launch phase accident: high temperatures, shrapnel, and explosive over-pressure. However, the essential problem is that NASA engineers have failed to perform a full-scale, realistic test of an explosion involving the RTGs.
In other areas of engineering, we have a good understanding of what happens when many different types of catastrophes happen, e.g. plane crashes and train wrecks, because we have a large body of experimental data. However, we have no experimental data by which to estimate the true dispersion of plutonium during a launch phase explosion because no realistic tests have ever been conducted.
NASA, however, has conducted some partial tests, which already reveal the vulnerability of the RTGs to extreme environments. The FEIS in fact, concedes that plutonium will escape the RTGs during a launch phase explosion, but its analysis is purely hypothetical and results in only a rough estimate.
In particular, we find:
- i) High temperatures. The iridium casing surrounding the RTGs begins to oxidize and degrade at 1,000 degrees C, and begins to melt at 2,425 degrees C. Graphite eutectic melting points are even lower: 2,269 C. Experiments with the fuel cladding show that they may resist temperatures of about 2,360 C found in propellant fires, which is just 65 degrees below the melting point of the iridium casing, but are expected to fail beyond that.
  Several conclusions can be drawn:
  - The laws of thermodynamics show that there is a statistical distribution of molecules at kinetic energies beyond the average one, given by the Maxwell-Boltzmann distribution, indicating that structurally the iridium casing will begin to soften and weaken even as it approaches its melting point. In other words, the structural integrity of the iridium casing will degrade as it approaches its melting point and make it possible for shrapnel and explosive over-pressure to burst open the casing. Thus, the combination of temperature, shrapnel, and over-pressure may be sufficient to burst most of the containers wide open.
  - Temperatures even beyond 3000 degrees C can typically be found locally in chemical explosions and reactions (e.g. an acetylene torch typically burns at 3,315 C). This is well beyond the melting point of the iridium casing. As a rough estimate, we know from the Stefan-Boltzmann and Wien's law that the color of a flame is roughly correlated with temperature, and the color red typically found in combustive reactions (at wavelengths of 7,000 angstroms) will be correlated with temperatures of about 4,000 C. Thus, we can expect some melting of the iridium casing due to local heating within the fireball, although the average temperature may be lower than the melting point.
- ii) Shrapnel. Tests have shown that aluminum bullets fired at the RTGs at velocities of 1,820 ft/sec and titanium bullets fired at l,387 ft/sec have caused a breach of containment. Edge-on fragments at velocities as low as 312 ft/s can rupture the leading fuel clads. So even at room temperature, we can expect high-velocity fragments to pierce the RTGs. But at high temperatures near the melting point of iridium, where the RTG casings are weakened by high temperatures and pressures, we can expect shrapnel to do even more damage to the RTG casings, bursting many of them open.
- iii) Over-pressure. Chemical explosions can cause local over-pressures of several thousand pounds per square inch. The RTGs have been tested to 2,210 lb/ft^2 without fuel release. However, under the weakened conditions created by high temperature, shrapnel, etc., it is not known how much can actually escape.
  The point is that a full-scale test involving the simultaneous conditions of high temperature, shrapnel, and over-pressure has never been done. It is likely that the combination of all three will cause severe rupturing of the RTGs.
  In spite of all these factors and uncertainties, the FEIS on p. 4-48 confidently concludes that a maximum of 28.7 curies, or less than .01% of the plutonium, will escape during a launch phase accident.
  Several points can be made:
  - This estimate is sheer speculation. The number is made up. Since no one has ever done a full-scale test of the RTGs in the explosive environment of a booster rocket failure, it pure guesswork as to how much plutonium will escape.
  - However, the estimates are given as a statement of fact, with no error bars or indications of reliability. We have no indication of the confidence level of this number. This is a severe statistical mistake.
  - The figure of 28.7 curies of plutonium is given to three significant figures, which is rather surprising, revealing a lack of grasp of statistical analysis on the part of the engineers. According to the laws of statistics, the propagation of errors determines that a calculation is no more reliable than its largest source of error. The largest source of error in this calculation is the fact that the engineers have made up many of the numbers out of thin air. Thus, calculating the plutonium release to three significant figures reveals a remarkable lack of understanding of even elementary statistics.
  - Given the fact that the simultaneous effect of high temperature, shrapnel, and over-pressure has never been fully tested, and given the fact that in combination they will probably cause a large failure of the iridium casing, a figure of 30% to 40% release is probably more realistic.
b) Area of Impact.
In typical radiological computer programs conducted by the military and the commercial nuclear industry, the area of impact of the accident is largely a function of wind conditions. Computer calculations involve solving a simple second-order partial differential equation (the standard Helmholtz equation with source term) by iterations. Because we have the conservation of mass, the source term is the driving term within this second order differential equation, sometimes called the diffusion equation.
In addition, actual experiments have shown that micron-sized particles of natural uranium, U-238, can be dispersed by the wind over 25 miles. In nuclear power plant accidents, radiation has been dispersed several thousand miles from the original accident. (For example, in the Windscale disaster in England in 1957, which was completely hushed up by British authorities, the radioactive cloud emerging from the carbon-moderate reactor was tracked going over London, sailing over the English channel, and finally dispersing over Cairo, Egypt. More recently, the radiation from Chernobyl was widely tracked over Europe and even the U.S.)
However, what is rather remarkable is that the FEIS totally ignores wind conditions and merely postulates that the plutonium will be dispersed, in one scenario, within an area of 7.18 x 10^-2 square miles. This is a roughly a square area 1,000 feet on each side. Again, the fact that this is presented without any error bars, and to three significant figures, shows the ignorance of the engineers who calculated this number.
But what is revealing is that the FEIS assumes that almost all the plutonium will be confined to the launch facility. According to the FEIS, no plutonium is expected to leave the launch pad area. In other words, NASA engineers have discovered a new law of physics: the winds stop blowing during a rocket launch.
But anyone who lived through the Challenger explosion, the Delta rocket explosion, etc., will realize that debris has been pulverized and spread over a significant area. Eyewitness accounts of the recent Delta rocket explosion indicated debris scattered over several miles.
In fact, experiments conducted on metal oxides have shown that a significant percent of the inventory can be pulverized into a fine dust of micron-sized particles, which can then be blown miles from the original site by the winds. These micron-sized particles are especially dangerous because they stay lodged deeply in the lungs for decades, where ciliary action is useless in expelling these particulates. Thus, these particles can emit radiation at close range to nearby lung tissue for decades to come, causing cancer.
c) Population density.
Yet another reason for attaining low estimates of risk is the FEIS's assumption that the population density is rather low. In this calculation, one problem is determining the number of person-rems which will initiate a cancer. One can reasonably assume that 5,000 person-rems will induce a single cancer. (Although some critics have placed the true figure as low as 300 person-rems/cancer.)
However, what is in dispute is the fact that the FEIS assumes a rather average density of people per square mile. This is therefore not a maximum credible accident, which would assume that the winds blow the plutonium into a major city.
For example, the FEIS assumes that, for a Phase 5 accident over Africa, the expected health risk would be 1.5 x 10^-4 over a population of only 1,000 people. This is low even for Africa. Not to mention that the rocket may misfire during the launch phase and tumble in a partial orbit, thereby landing almost anywhere on the earth, rather than in Africa.
A Phase 1 accident would release plutonium in an area populated by only 100,000 people. But if the winds blow, then the area affected within 5 counties of the launch site could total over a million people.

B. Fly-by Phase (VVEJGA Phase)

The source of greatest concern, from the point of view of plutonium release, is the fly-by. The Cassini probe will be whipping around the earth at around 40,000 miles per hour, significantly faster than the escape velocity of the earth (25,000 miles per hours) and faster than many meteorites. If there is even the tiniest miscalculation of the trajectory, the Cassini may burn up in the atmosphere and spray a significant portion of land area with plutonium. There is ample experimental evidence that space probes, without heat shields, will vaporize upon re-entry. However, the FEIS again takes a low estimate of plutonium release.

a) Source term.
The FEIS admits that about 32% to 34% of the plutonium is expected to be released high in the atmosphere. However, the FEIS then dismisses this factor by diluting it over the population of the entire earth. This neglects the fact that the mixing of plutonium in the atmosphere takes a considerable amount of time, and in the meantime it may concentrate or hover over certain regions of the earth. This effect is ignored by the FEIS.
The FEIS then calculates how much plutonium may actually land on the earth, and again underestimates the real risks.
The FEIS first divides the source term into three parts: a rock impact, soil impact, and water impact, and then calculates the percent distribution of each on the planet earth. For example, the FEIS estimates that 4% will hit rock, 21% will hit soil, and 75% will hit water.
This is a rather odd way of calculating maximum risks, because it confuses probability of an accident with the consequences of that accident. The calculation of how much surface area of the earth is divided into rock, soil, and water belongs in a calculation of the probability of mishap, not in the calculation of maximum risk.
The calculation of maximum credible risk necessarily assumes maximum risk by definition, i.e. that all the plutonium will hit rock, since that is the maximum credible scenario. Rather than 4% of the plutonium hitting rock, one should assume that all of it does.
Second, the FEIS calculates the percent of plutonium that can be released on impact with rock, soil, and water. Again, these numbers are simply pulled out of a hat, with no justification. For example, in one scenario, it assumes that all of the plutonium will be dispersed if it hits rock, 25% of the plutonium hitting soil will escape, and none hitting water will escape. However, no justification is given for these estimates, because there are none.
The important point is that no one has ever done an experiment calculating the effect of entering the atmosphere with RTGs at 40,000 miles per hour. Until this experiment is done (using a replacement for plutonium), all these numbers are purely speculative.
b) Area of impact
The estimated land contamination for this plutonium accident is on the order of 2,000 sq. km. That is roughly equivalent to a square about 27 miles on a side.
More recently, on April 1997, the Supplemental Environmental Impact Statement has revised the early estimate of cancer fatalities from 2,300 to 120 (p. 2-19). This may seem strange, until one realizes that their assumptions have become even more conservative. Instead of assuming that land contamination can be 2,000 sq. km, the new estimate puts it at a surprisingly small area of 7.9 sq. km. This is a square about 1.7 miles on each side. In other words, the new EIS assumes that the Cassini probe, coming down in flames from outer space at 40,000 miles per hour, will hit a bull's eye and then remain there, without any winds whatsoever.
This is a remarkable reduction by a factor of 250, which once again is pulled out of a hat, without any justification. Not surprisingly, the casualty figures have also dropped significantly, from 2,300 to 120, a factor of 20.
c) Population density
Again, the FEIS assumes average figures for population density, and totally neglects the fact that there are large population concentrations on the earth where tens of millions live. Within a 50 mile radius of Manhattan, for example, there are about 20 million people, or about 8% of the entire population of the U.S. Similarly, there are other concentrations of people on the earth with even larger densities, such as around Tokyo, Mexico City, and Shanghai.

III. Calculation of Risk

The analysis used by the EIS to calculate the probability of a maximum accident with the Cassini mission uses methods pioneered by the nuclear power industry (e.g. single event failures, event tree analysis, Monte Carlo calculations, etc.)

Although these methods are standard for the field, these methods have largely been discredited by the actual operating record of nuclear power accidents. Three Mile Island, for example, was a Class IX accident which was largely unforeseen by MIT's WASH-1400, the standard reference within the industry, which largely ignored small pipe breaks.

The methodology is flawed for several reasons:

i) Human error and design flaws.
Most of the major accidents that have taken place in the past are beyond the simple-minded event-tree analysis of the FEIS. For example, one can design a car such that the chances of an accident approach a million to one, with air bags, anti-lock brakes, seat belts, etc. However, this does not foresee the fact that someone might drive this car over a cliff.

The actual track record of accidents shows that computer calculations are often misleading and give a false sense of confidence:

Three Mile Island was caused by human error (misreading the PORV valve light on the control panel) and design flaws (lack of a water gauge meter in the containment vessel and poor design of the PORV warning light). It was not foreseen by WASH-1400, which concentrated on large pipe brakes.
The Chernobyl disaster was caused by human error, when the engineers and managers manually disengaged the control rods. There were also design flaws, since the carbon-moderated reactor was prone to a positive reactivity power surge. During the accident, when a transient sent power levels rising, the lack of a SCRAM system caused neutron levels to rise exponentially, causing a steam/hydrogen gas explosion which blew the top the reactor.
The Hubble Space Telescope was launched into space with incorrectly ground mirrors. This mishap was also caused by human error. Part of the fault, among others, lies in a worker who inserted a ruler in backwards in Danbury, Connecticut, where the mirror was being machined, thereby making possible an incorrect shape for the mirror. Remarkably, the flaw was later detected, but ignored by engineers. It was not noticed until the mirror was launched into space, causing a billion dollar public relations disaster.
Star Wars. In a well-known mishap, the Space Shuttle was conducting a test of the Star Wars laser system, with a laser beam sent from Hawaii. Because of human error (converting miles to meters incorrectly), the Shuttle was oriented in space away from Hawaii, not towards it, and missed the signal completely.

The real danger is that the engineers begin to believe their own computer calculations, which are only a guide, not a law of nature. Then they become overconfident and fail to foresee the inevitable.

ii) GIGO. There is an expression, "garbage in, garbage out." Even if you use the world's largest supercomputer, if your assumptions are faulty, then your conclusions will also be faulty. For example, one can use a supercomputer to calculate the precise number of angels that can dance on the head of a pin. But giving you this number to three significant figures is meaningless, since the original assumption was in question.

iii) Similarly, the basic assumption of the FEIS is that one can model accidents on the basis of single event failures, when multiple failures, common mode failures, human error, and design flaws have contributed to most accidents. Unfortunately, it is beyond the power of computers to realistically model these more complex types of accidents.

iv) Weakest link: the Titan IV
A chain is no stronger than its weakest link. The weakest link is the Titan IV booster rocket, which has a failure rate of about one in 20. And booster rockets in general have a failure rate of 1 in 70 or so. Furthermore, there have been 3 failures among the 23 missions involving plutonium power packs, one which released a significant amount of radiation. In fact, everyone on the earth has a piece of the SNAP 9A satellite in their body. The SNAP 9A satellite also significantly increased the amount of plutonium-238 on the planet earth.

v) Where does the one-in-a-million figure come from?
The FEIS typically has accident probabilities in the range of one-in-a-million. By analyzing the calculation, one can see where this figure comes from. One can see that most of the one-in-a-million comes from the impact of a micrometeorite on the Cassini probe. In the FEIS, very little of the probability comes from errors in transmission, errors from ground control, etc. This patently violates the actual experience with space probes.

Meteorite damage is of a real concern, but human and technical flaws are much more likely to cause failure. For example, it has been recently estimated that the International Space Station Alpha may suffer a 50% probability of a catastrophic meteor impact during its 15 year life span. This is certainly a significant danger. But actual operating experience has shown that in almost all space missions, the real danger comes from human and technical flaws, i.e. sending the wrong instructions to space probes, failure of transmitters and solar panels to unfurl correctly, etc. These are almost impossible to model by computer.

vi) Furthermore, a one-in-a-million figure assumes that one million Cassini space probes have been fired into space, and only one Cassini space probe malfunctioned. This is clearly untrue. In other words, the table of probability given by NASA is just a wish list. The one-in-a-million figure is wishful thinking masquerading as reputable science.

IV. Calculation of Alternatives

The FEIS undertakes a half-hearted effort to calculate alternatives to using plutonium. Since only 800 watts of power need to be replaced, or the output of roughly eight light bulbs, the alternatives must be taken seriously.

There is no question that, in deep space, there is not much sunlight. At the distance of Saturn, there is only 1% of the solar flux found on the planet earth (in watts/sq. meter). The debate revolves around whether solar/fuel cells can make up the 800 watts necessary to run the mission.

The FEIS on p. 2-56 claims that, if the Cassini is equipped with massive, bulky solar panels, the probe will be 130 pounds too heavy for lift-off. (The Titan IV can lift 13,743 pounds of payload to Saturn). However, the calculation is incomplete, since it does not consider some simple options:

Downsize the craft. If the probe is 130 pounds overweight, then the obvious solution is to lose 130 pounds of equipment. This means leaving out some experiments. However, the Cassini is the Cadillac of space missions, and a few less redundant experiments will still give us excellent science. This may be the solution.

Conform to the new NASA philosophy. The new philosophy of NASA is faster, cheaper, better. For example, the Mars Observer was a billion dollar fiasco: bulky, costly, infrequent. The new Mars probes were correctly downsized; the new strategy is to send small space craft to Mars twice every two years. Similarly, space shots to Saturn should be downsized and made more frequent, not less frequent, and energized by solar cells.

Cassini is therefore a left-over from the old NASA philosophy of doing big space shots once every 10 years. Since space probes were so infrequent, this philosophy resulted in space craft that were overloaded with experiments, and hence the RTGs seemed a natural solution. But the new philosophy of NASA should generate small, frequent, and cheap probes to Saturn which are well within the capability of solar power.

Saturn is not going away. All this will cause delays, but Saturn is not going to go away. Other windows of opportunity will open up. Given the fact that one can whip around other planets and change trajectory, windows of opportunities open up all the time.

Use a combination of solar/fuel cells. The FEIS only considers solar and fuel cells separately, not in conjunction. Fuel cells can be used to store energy when solar cells can no longer receive adequate energy from the sun.

V. Conclusion and recommendations:

We all live in a world of risks. Every day, when we enter cars or airplanes, we place our bodies at risk. Therefore, we must be careful in how risks are handled.

But the difference with the Cassini mission is that we voluntarily put ourselves at risk when traveling. However, no one asked the American people if they wanted to put themselves in danger. NASA bureaucrats, not the American people, are making this decision.

Second, if we are in a car accident, only a handful at most will die. But no one told the American people that thousands may die if a plutonium accident takes place.

Similarly, the FEIS justifies the figure of 2,300 cancer deaths by stating that that figure is lost in the background cancer levels found world-wide. This is a strange argument. That same argument can be used to justify mass murder. Since thousands die violent deaths in the U.S., it makes no difference if a few hundred more die by a serial killer. They will be lost in the background noise.

Of course, we all want a healthy, vibrant space program to explore the universe. However, it should also be made safe. Since the American taxpayers are paying for it, they have a right to know the true risks, and should be informed of the debate concerning accident risks within the scientific community.

Unfortunately, the American people, being constantly told that the probability of an accident is on the order of one in a million or a one in a billion, will feel betrayed when a catastrophic accident does occur in space. Such a space tragedy could cause a backlash from the American people, who will correctly feel that they were lied to by NASA bureaucrats. This could be the end of the space program, which would be a disaster to science.

Furthermore, there is no mention of property damage in such an accident. The Three Mile Accident, for example, reputedly released just 13 curies of iodine (compared to 400,000 curies in the Cassini mission) yet it generated two billion dollars in law suits.

Even if no significant amounts of radiation are released in a plutonium accident, property values are expected to plummet. And if significant amounts of plutonium are released, then whole areas must be quarantined, earth dug up and placed in 55 gallon drums, houses hosed down with fire trucks, crops impounded, etc. That was one terrible lesson from Chernobyl. The loss to home owners and the agribusiness in the area around the Cape could amount to tens of billions of dollars.

Therefore, the mission of a critic is to save the space program from NASA bureaurcrats.

Unfortunately, NASA commits the worst mistake that a scientist can ever make: believing your own press release. A casual observer, reading the FEIS, may be deceived into thinking that a careful analysis has been done. But when actually reproducing the calculation, the observer will be shocked at how many guesses, hidden assumptions, and minimizations of risks there are in the FEIS.

A true scientist carefully writes down the error bars and the confidence level he or she places in their figures. A careful scientist does not do what NASA has done:

a) fail to perform full-scale accident tests
b) pull numbers out of hat to compensate for this ignorance
c) dress up these fake numbers with complex computer pro- grams that cannot measure the true risks from human error, etc.
d) publish the results with an accuracy of 3 significant figures, with no mention of error bars, confidence levels, or a list of assumptions.

This borders on scientific dishonesty.

It is no accident, therefore, that the FEIS comes up with consistently low numbers for a maximum accident.

The simplest way to solve our problem is to use solar cells with fuel cells. This will require downsizing the space craft by at least 130 pounds. But this is also in tune with the new philosophy of faster, better, and cheaper. The Cassini mission, however, is a relic of the old thinking of slower, more expensive, less frequent.

A new program to explore the planets would have these probes downsized and launched much more frequently, using non-nuclear energy sources.

In the interim, this may cost more and cause some delays, but it may also have the lives of thousands, prevent law suits numbering in the tens of billions, and save the space program from NASA bureaurcrats.

VI. Short biography

Dr. Michio Kaku is the Henry Semat professor of theoretical physics at the Graduate Center of the City Univ. of New York. He is one of the world's leading authorities on Einstein's Unified Field Theory. He is the co-founder of string field theory. His textbooks on quantum field theory, superstring theory, quantum gravity, and conformal field theory are used by Ph.D. students in leading institutions around the world. He has lectured to the Soviet Academy of Sciences in Moscow, at Oxford Univ., Cambridge Univ., Univ. of Rome, the Univ. of Tokyo, and CERN in Geneva, Switzerland.

He received his B.A. in physics from Harvard in 1968. He graduated summa cum laude (with highest honors), Phi Beta Kappa, and number one in his physics class.

He received his Ph.D. at the Radiation Laboratory at the Univ. of Calif. at Berkeley in 1972. He was a research associate at Princeton University in 1973, and has been a professor at CUNY for the past 25 years. He has been a visiting professor at Cal Tech, the Institute for Advanced Study at Princeton, and New York University.

He has published 9 books and 70 articles in the scientific literature (including Nuclear Physics, Physical Review, Physics Letters, Physical Review Letters).

He is a Fellow of the American Physical Society, and honor held by the top 10% of physicists in the U.S.

Reprinted online by permission of Dr. Michio Kaku.

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First placed online August 9th, 1997.
Last modified October 5th, 1997.
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