Freeman Dyson

One of the big turning points in my life was a meeting withEnrico Fermi in the spring of

1953. In a few minutes, Fermi politelybut ruthlessly demolished a programmeof research that my students and I hadbeen pursuing for several years. Heprobably saved us from several moreyears of fruitless wandering along a roadthat was leading nowhere. I am eternallygrateful to him for destroying our illusions and telling us the bitter truth.

Fermi was one of the great physicistsof our time, outstanding both as a theorist and as an experimenter. He led the team that built the first nuclearreactor in Chicago in 1942. By 1953 he was head of the team that built the Chicago cyclotron, and was using it to explore the strong forces that hold nuclei together. He made the first accurate measurements of the scattering of mesons by protons, anexperiment that gave the most directevidence then available of the nature ofthe strong forces .

At that time I was a young professorof theoretical physics at Cornell Univer-sity, responsible for directing theresearch of a small army of graduate students and postdocs. I had put them to work calculating meson–proton scat-tering, so that their theoretical calculationscould be compared with Fermi’s measure-ments. In 1948 and 1949 we had made similar calculations of atomic processes,usingthe theory of quantum electrodynamics,andfound spectacular agreement between experi-ment and theory.Quantum electrodynamicsis the theory of electrons and photons interacting through electromagnetic forces.Because the electromagnetic forces are weak,we could calculate the atomic processes precisely. By 1951, we had triumphantly finished the atomic calculations and werelooking for fresh fields to conquer. We decided to use the same techniques of calcu-lation to explore the strong nuclear forces.We began by calculating meson–proton scattering, using a theory of the strong forcesknown as pseudoscalar meson theory. By thespring of 1953, after heroic efforts, we hadplotted theoretical graphs of meson–protonscattering.We joyfully observed that our calculated numbers agreed pretty well withFermi’s measured numbers. So I made an appointment to meet with Fermi andshow him our results. Proudly, I rode theGreyhound bus from Ithaca to Chicago with

NATURE | VOL 427 | 22 JANUARY 2004 | www.nature.com/nature 297

physical picture, and the forces are so strong that nothing converges. Toreach your calculated results, you had to introduce arbitrary cut-off proce-dures that are not based either on solidphysics or on solid mathematics.”

In desperation I asked Fermi whetherhe was not impressed by the agreementbetween our calculated numbers and hismeasured numbers. He replied, “Howmany arbitrary parameters did you usefor your calculations?” I thought for amoment about our cut-off proceduresand said, “Four.” He said, “I remembermy friend Johnny von Neumann used tosay, with four parameters I can fit an elephant, and with five I can make himwiggle his trunk.”With that, the conver-sation was over. I thanked Fermi for histime and trouble,and sadly took the nextbus back to Ithaca to tell the bad news to the students.Because it was importantfor the students to have their names on a published paper, we did not abandonour calculations immediately. We

finished them andwrote a long paperthat was duly pub-lished in the Physi-cal Review with allour names on it.Then we dispersedto find other lines ofwork. I escaped toBerkeley, California,to start a new careerin condensed-matterphysics.

Looking back afterfifty years, we canclearly see that Fermiwas right. The crucialdiscovery that madesense of the strongforces was the quark.Mesons and protons are

little bags of quarks. Before Murray Gell-Mann discovered quarks, no theory of thestrong forces could possibly have been adequate. Fermi knew nothing about quarks,and died before they were discovered. Butsomehow he knew that something essentialwas missing in the meson theories ofthe 1950s. His physical intuition told himthat the pseudoscalar meson theory couldnot be right. And so it was Fermi’s intuition,and not any discrepancy between theory andexperiment, that saved me and my studentsfrom getting stuck in a blind alley. ■

Freeman Dyson is at the Institute for Advanced Study,Einstein Drive, Princeton, New Jersey 08540, USA.

A meeting with Enrico Fermi

a package of our theoreticalgraphs to show to Fermi.

When I arrived in Fermi’soffice, I handed the graphs toFermi, but he hardly glancedat them. He invited me to sitdown, and asked me in afriendly way about the healthof my wife and our new-born baby son, now fiftyyears old. Then he deliveredhis verdict in a quiet, even voice. “There aretwo ways of doing calculations in theoreticalphysics”, he said. “One way, and this is the way I prefer, is to have a clear physical pictureof the process that you are calculating. Theother way is to have a precise and self-consistent mathematical formalism. You have neither.” I was slightly stunned, but ventured to ask him why he did not considerthe pseudoscalar meson theory to be a self-consistent mathematical formalism. Hereplied, “Quantum electrodynamics is a good theory because the forces are weak,and when the formalism is ambiguous wehave a clear physical picture to guide us.Withthe pseudoscalar meson theory there is no

essay turning points

How one intuitive physicist rescued a team from fruitless research.

Crossed paths: A discussion with EnricoFermi (above) made Freeman Dyson(right) change his career direction.

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© 2004 Nature Publishing Group

© 2004 Nature Publishing Group

There is a famous aphorism in physics: ‘‘Give mefour parameters and I can fit an elephant. Giveme five and I can wag its tail’’ [5].

[5] We have tried to find the appropriateattribution for this quote but have beenunsuccessful. Variants of the statement (differingin the number of parameters) have beenattributed to C.F. Gauss, Niels Bohr, LordKelvin, Enrico Fermi, and Richard Feynman.

Excerpted from:Kevin S. Brown and James P. Sethna. 2003.Statistical mechanical approaches to models withmany poorly known parameters. Physical ReviewE 68: 021904.

1.4 Inference and the Principle of Parsimony 29

ously. The advent of Markov chain Monte Carlo methods (Gilks et al. 1996,Gamerman 1997) may soon give rise to a general but practical framework forspatiotemporal modeling; model selection will be an important component ofsuch a framework. A step towards this general framework was made by Buck-land and Elston (1993), who modeled changes in the spatial distribution ofwildlife.

There are many other examples where modeling of data plays a fundamen-tal role in the biological sciences. Henceforth, we will exclude only modelingthat cannot be put into a likelihood or quasi-likelihood (Wedderburn 1974)framework and models that do not explicitly relate to empirical data. All leastsquares formulations are merely special cases that have an equivalent likeli-hood formulation in usual practice. There are general information-theoreticapproaches for models well outside the likelihood framework (Qin and Law-less 1994, Ishiguo et al. 1997, Hurvich and Simonoff 1998, and Pan 2001aand b). There are now model selection methods for nonparametric regression,splines, kernel methods, martingales, and generalized estimation equations.Thus, methods exist for nearly all classes of models we might expect to see inthe theoretical or applied biological sciences.

1.4 Inference and the Principle of Parsimony

1.4.1 Avoid Overfitting to Achieve a Good Model Fit

Consider two analysts studying a small set of biological data using a multiplelinear regression model. The first exclaims that a particular model provides anexcellent fit to the data. The second notices that 22 parameters were used inthe regression and states, “Yes, but you have used enough parameters to fit anelephant!” This seeming conflict between increasing model fit and increasingnumbers of parameters to be estimated from the data led Wel (1975) to answerthe question, “How many parameters does it take to fit an elephant?” Wel findsthat about 30 parameters would do reasonably well (Figure 1.2); of course,had he fit 36 parameters to his data, he could have achieved a perfectfit.

Wel’s finding is both insightful and humorous, but it deserves further inter-pretation for our purposes here. His “standard” is itself only a crude drawing—iteven lacks ears, a prominent elephantine feature; hardly truth. A better targetwould have been a large, digitized, high-resolution photograph; however, this,too, would have been only a model (and not truth). Perhaps a real elephantshould have been used as truth, but this begs the question, “Which elephantshould we use?” This simple example will encourage thinking about full re-ality, “true models,” and approximating models and motivate the principle ofparsimony in the following section. William of Occam suggested in the four-teenth century that one “shave away all that is unnecessary”—a dictumoften referred to as Occam’s razor. Occam’s razor has had a long history

Excerpted from: Kenneth P. Burnham and David R. Anderson. 2002. Model Selection and Multimodel Inference: A Practical Information-theoretic Approach. 2nd ed. New York: Springer.

30 1. Introduction

FIGURE 1.2. “How many parameters does does it take to fit an elephant?” was answeredby Wel (1975). He started with an idealized drawing (A) defined by 36 points and usedleast squares Fourier sine series fits of the form x(t) � α0 +∑

αi sin(itπ/36) and y(t) �β0 +∑βi sin(itπ/36) for i � 1, . . . , N . He examined fits for K � 5, 10, 20, and 30 (shownin B–E) and stopped with the fit of a 30 term model. He concluded that the 30-term model“may not satisfy the third-grade art teacher, but would carry most chemical engineers intopreliminary design.”

in both science and technology, and it is embodied in the principle of par-simony. Albert Einstein is supposed to have said, “Everything should be madeas simple as possible, but no simpler.”

Success in the analysis of real data and the resulting inference often dependsimportantly on the choice of a best approximating model. Data analysis in thebiological sciences should be based on a parsimonious model that provides anaccurate approximation to the structural information in the data at hand; thisshould not be viewed as searching for the “true model.” Modeling and modelselection are essentially concerned with the “art of approximation” (Akaike1974).

Drawing an elephant with four complex parameters Jurgen Mayer Max Planck Instilflte of Molecular Cell Biology and Genetics, Pjotenilauerstr. 108, 01307 Dresden, Germany

Khaled Khairy European Molecular Biology La.boratory, MeyerhofstrafJe. 1, 69117 Heidelberg, Gennany

Jonathon Howard Max Planck Institute of Molecular Cell Biology and Genetics, Pfotellhauerstr. 108, 01307 Dresden, Germany

(Received 20 August 2008; accepted 5 October 2009)

We define four complex numbers representing the parameters needed to specify an elephantine shape. The real and imaginary parts of these complex numbers are the coefficients of a Fourier coordinate expansion, a powerful tool for reducing the data required to define shapes. © 2010 American Association of PhYSics Teacllel'.r. [DOl: 10.1119/1.3254017]

A turning point in Freeman Dyson's life occurred during a meeting in the Spring of 1953 when Enrico Fermi criticized the complexity of Dyson's model by quoting Johnny von Neumann:' ''With four parameters I can fit an elephant, and with five [ can make him wiggle his trunk." Since then it has become a well-known saying among physicists, but nobody has successfully implemented it.

trace out elJiptical corrections analogous to Ptolemy's epicycles.' Visualization of the corresponding elJipses can be found at Ref. 6.

To parametrize an elephant, we note that its perimeter can be described as a set of points (x(t),y(t)), where t is a pa­rameter that can be interpreted as the elapsed time while going along the path of the contour. If the speed is uniform, t becomes the arc length. We expand x and y separately2 as a Fourier series

x(t) = 2: (A% cos(kt) + B:l sin(kt)) , k=O

yet) = 2: (A~ cos(kt) +B~ sin(kt)) , k=O

(1)

(2)

where Ai, 11k, Ak. and EX are the expansion coefficients. The lower indices k apply to the kth term in the expansion, and the upper indices denote the x or y expansion, respectively.

Using this expansion of the x and y coordinates, We can analyze shapes by tracing the boundary and calculating the coefficients in the expansions (using standard methods from Fourier analysis). By truncating the expansion, the shape is smoothed. Truncation leads to a huge reduction in the infor­mation necessary to express a certain shape compared to a pixelated image, for example. Szekely et al.' used this ap­proach to segment magnetic resonance imaging data. A simi­lar approach was used to analyze the shapes of red blood cells: with a spherical harmonics expansion serving as a 3D generalization of the Fourier coordinate expansion.

The coefficients represent the best fit to the given shape in the following sense. The k=O component corresponds to the center of mass of the perimeter. The k= I component Corre­sponds to the best fit ellipse. The higher order components

648 Am. I. Phys. 78 (6). Iune 20tO http://oupl.org/.ljp

We now use this tool to fit an elephant with four param­eters. Wei' tried this task in 1975 using a least-squares Fou­rier sine series but required about 30 terms. By analyzing the picture in Fig. 1(a) and eliminating components with ampli­tudes less than 10% of the maximum amplitude, we obtained an approximate spectrum. The remaining amplitudes were

Pattern (a) 2Or---·--·-·-------·-·--·-.. -----.. ··j 40t ·i

I ! , !

:.. GOt 1

i i 8O~ i

1001 : ! ,

120L. __ .. _ .. _"'"_._ .... ______ . __ .... ,. __ . ___ .......... __ ._ .... _____ .1 50 100 150 200

x

(b)100

50

Y

-50

-1°B - 00 -50 0 50 100 x

Fig. 1. (a) Outline of an eJephnnt. (b) Three snapshots of the wiggling trunk.

Q) 20 I 0 American Association of Physics Teachers 648

Table I. The five complex parameters PI,'" ,Ps that encode the elephant including its wiggling trunk.

Parameter

PI::::50-30i Pl=18+8i P3=12-IOi P4=-14-60i Ps=40+20;

Real part

81=50 ill=18 A3=12

Aj=-14 Wiggle coeff.=40

Imaginary part

B{=-30

B~=8 8~=-1O

A)=-60 xcyc =Ycyc::::20

slightly modified to improve the aesthetics of the final image. By incorporating these coefficients into complex numbers, we have the equivalent of an elephant contour coded in a set of four complex parameters (see Fig. l(b)).

Thc real part of the fifth parameter is the "wiggle param­eter," which determines the x-value where the trunk is at­tached to the body (see the video in Ref. 8). Its imaginary part is used to make the shape more animal-like by fixing the coordinates for the elephant's eye. All the paranleters are specified in Table I.

The resulting shape is schematic and cartoonlike but is still recognizable as an elephant. Although the use of the Fourier coordinate expansion is not new,2,3 our approach clearly demonstrates its usefulness in reducing the number of parameters needed to describe a two-dimensional contour. In

649 Am. 1. Phys .• Vol. 78, No.6, June 2010

the special case of fitting an elephant, it is even possible to lower it to four complex parameters and therein implement a well-known saying.

ACKNOWLEDGMENTS

Many thanks to Jean-Yvcs Tinevez and Marija Zanie, as well as the anonymous reviewers, for revising and improving this article.

IF. Dyson, "A meeting with Enrico Fermi," Nature (London) 427(6972), 297 (2004).

2F. P. Kuhl and C. R. Giardina, "Elliptic Fourier features of a closed contour," Comput. Graph. Image Process. 18, 236-258 (1982).

JG. Szekely, A. Kelemen, C. Brechblihler, and G. Gerig, "Segmentation of 2D and 3D objects from MRI volume data using constrained elastic de­formations of flexible Fourier contour and surface models," Merl. Image Anal. 1(1), 19-34 (1996).

4K. Khairy and 1. Howard, "Spherical hlUTl1onics-based parametric decon­volution of 3D sutface images using bending energy minimization," Med. Image Anal. 12(2),217-227 (2008).

sThe interactive Java applet written by Rosemary Kennett, (physics.syr.edu/courses/javaldemoslkennettJEpicyclelEplcycle.html).

6Interactive Java appJet of elliptic descriptors by F. Puente Le6n, (www.vms.ei.tum.de/Iehre/vrns/fourierf).

' J, Wei, "Least square fitting of an elellhant." CHEMTECH S. 128-129 (1975).

8See supplementary material at http://dx.doLorglJO.tl19/1.3254017 for the movie showing the wiggling trunk.

Notes and Discussions 649

478 nature physics | VOL 6 | JULY 2010 | www.nature.com/naturephysics

research highlightsFitted at last Am. J. Phys. 78, 648–649 (2010)

In the spring of 1953, Freeman Dyson travelled to Chicago to meet Enrico Fermi. In his luggage, the young professor had the results of his group’s long effort to calculate meson–proton scattering. But Fermi was not impressed, even if the agreement of Dyson’s calculations with experimental data obtained at the Chicago cyclotron was good. Fermi didn’t trust the arbitrary parameters used in the calculations: “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”

Dyson took Fermi’s point seriously, and changed his career direction. (“I am eternally grateful to him”, Dyson said half a century later, “for destroying our illusions and telling us the bitter truth.”) But still — can the outline of an elephant be really defined with only four parameters? An early attempt at implementing that task with least-square fits failed. But Jürgen Mayer and colleagues have now succeeded, using appropriate truncated Fourier expansions. With four complex parameters, they describe a curve that can be interpreted as ‘elephantine’ (pictured). And with a fifth parameter, they can control both the position of the trunk and the position of the eye.

On-demand entanglementNature 465, 594–597 (2010)

An entangled-photon-emitting diode has been created by Cameron Salter and colleagues. An applied bias injects two electrons and two holes into a single indium arsenide quantum dot. The electron–hole pairs recombine in a cascade fashion that can follow one of two paths: the emission of a left-hand-polarized photon followed by a right-hand-polarized photon, or vice versa. As long as these two paths are indistinguishable, the two photons are

polarization-entangled. The team had to take special care to ensure that which-path information wasn’t available by another means — measuring the energy of the photons, for example — and that the cascade wasn’t interrupted by any rogue third electron.

The device has the advantage over the competing parametric down-conversion approach in that the process is deterministic, potentially enabling the creation of an entangled pair at the press of a button.

The work by Salter et al. is a beautiful combination of the two most important motivations for quantum-dot research: an electronic structure more complicated than ‘natural’ atoms leads to a richer array of physics, in this case entanglement; and solid-state approaches promise compact devices that don’t require a room full of expensive lasers.

hyperbolic spontaneityOpt. Lett. 35, 1863–1865 (2010)

Spontaneity usually isn’t easily controlled. One way to control an otherwise spontaneous process is through stimulation, as occurs in a nuclear chain reaction or a laser. Another is to change the environment in which the process occurs. This was one of the motivating concepts in the development of photonic crystals: if an excited fluorescent atom is placed in the centre of a material engineered to have no states for the atom to decay into, the atom should remain in its excited state indefinitely. The challenge has been to engineer a material with an effective and complete bandgap.

Mikhail Noginov and colleagues have taken the opposite approach. Rather than reduce the rate at which fluorescent atoms emit by limiting the density of states into

which they can decay, they enhance the emission rate by increasing the density of these states. They have demonstrated this by depositing a layer of laser-dye atoms onto a forest of silver nanowires embedded in a porous alumina template — a structure that has been predicted to behave as a so-called hyperbolic metamaterial with an anomalously high density of photonic states. The decay rate of the dye atoms increased by more than a factor of six. Such control is expected to be useful in the development of single-photon emitters.

Go retroMon. Not. R. Astron. Soc. doi:10.1111/j.1365-2966.2010.16797.x (2010)

At the centre of every galaxy is a supermassive black hole, surrounded by an accretion disk of gas and dust and possibly with jets streaming out of the plane of the disk. It had been thought that the faster the spin of the black hole, the more powerful the jets — but then some fast-spinning supermassive black holes were found to have no jets at all.

David Garofalo and colleagues think it’s not only about how fast the black hole spins, but in which direction. Black holes spinning in the same direction as their accretion disks — ‘prograde’ — may indeed have no jets, whereas the strongest jets are more likely to arise from a galaxy that has a ‘retrograde’ black hole, spinning in the opposite direction to its accretion disk.

Garofalo et al. show that the key is the gap between the black hole and its disk, which can be large for retrograde black holes, but decreases as the black hole, accreting material from the disk over time, evolves towards increasing prograde spin. Jet production is most effective for a large gap, which is associated with strong black-hole-threading magnetic fields.

x

y

A quantum spin liquid is a low-temperature state of an antiferromagnet in which quantum fluctuations prevent the spins ordering magnetically. The trouble is, how do you measure nothing? Several promising Heisenberg antiferromagnets show no magnetic order down to the lowest attainable temperatures — but it’s not possible to reach absolute zero to be sure. Minoru Yamashita and co-workers have addressed this limitation by probing the low-energy excitations of the organic insulator, EtMe3Sb[Pd(dmit)2]2, also known as dmit-131.

Heat conduction is an excellent probe of low-lying excitations. Indeed, the extrapolated zero-temperature thermal conductivity of dmit-131 has a term that is linear in temperature, which is the signature of gapless excitations such as those found in a standard metal. Given the insulating nature of the material, it is surprising to find gapless excitations. Moreover, the mean free path exceeds 1,000 times the distance between the spins, consistent with ballistic propagation. This and other properties of dmit-131 suggest a quantum state that is distinct from the ordered states that we know.

if a spin fluctuates in a forest Science 328, 1246–1248 (2010)

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Physics of elephant In the second half of the twentieth century, physicists formulated the so-called elephant conjecture, also called Ise’s conjecture. It states that given enough parameters one can fit an elephant, and with some more one can make the elephant wag its tail. The true author of Ise’s conjecture is not known, however, the conjecture has been repeated many times at many conferences and finally got attributed to Dr. W. Ise of MIT, who was known for having formulated many interesting conjectures; so it seemed logical to attribute this one to him too. Initially, Ise did not object. Many were mystified by the conjecture, calling it first interesting, then challenging and fascinating, and at some point it has become one of the most important and burning questions in contemporary physics. The breakthrough came when a student of zoology S. Loppy, who was charged with transporting by plane an elephant to the Pittsburgh ZOO, forgot to properly lock the cargo door, and the elephant fell down from high altitude creating an impressive crater in the Mohave Desert. Feeling guilty, the student promptly traveled to the crash site and measured the diameter and depth of the crater to be 10.5 and 2.2 meters, respectively. His seminal paper on the “First measurement of elephant by a high-energy collision” was immediately accepted for publication in Physical Review Letters. Before the physics community had a chance to ponder on the significance of this measurement, Professor M. Ensa of Princeton, who met Loppy on his return flight to Pittsburgh, formulated the first model of the elephant, and managed to publish it back-to-back with Loppy’s article. The model described the elephant as a sphere of diameter of 7.2 meters and mass of 5 metric tons. These two parameters described Loppy’s data beautifully. A possibility of using similar experimental set-up to better establish properties of the elephant was immediately realized in several scientific centers. Important research programs were started, grants were awarded, and systematic observations of el-craters, as they were now called, were pouring into scientific journals. In experiments, the intensity of elephant beams was customarily measured in MA (mega amperes) with a proviso that the elephant before discharging was charged with one electrical shock of 110V during 1 second. Translation tables to units using European voltage of 220V were also published. A substantial grant awarded within the European FP137 program allowed for a construction of the multi-laser device (MLD) to observe whether the elephant is hitting the ground headfirst or tail-first. After a short, but heated discussion, about including the Physics of elephant in Physical Review E, which seemed like a very logical step, the APS opted for a creation of a new section F. One of the principal subsections in this journal was named “Multifragmentation”. With the accumulated large body of experimental observations, Ise’s conjecture could now be put to a stringent experimental test. The first model of the elephant, using very many parameters, was created within the research program sponsored by SONY, and described the surface of the elephant with a fantastic resolution of 72 dpi and later even 300 dpi. Millions and next billions of parameters were adjusted to the experimental results obtained for el-craters. Very advanced statistical methods to look at confidence levels were applied in collaboration with mathematicians, and finally it became clear that Ise’s conjecture has been proven false. The article on that issue entitled “Ise proved wrong” was published in the New

Arctic FIDIPRO-EFES Workshop Hotel Riekonlinna, Saariselkä, Finland April 20-24, 2009 Future Prospects of Nuclear Structure Physics Workshop summary by J. Dobaczewski

York Times. At this point Ise issued a statement saying that he, in fact, never formulated the conjecture. Since results of measurements of el-craters were made available on the Internet, many scientists and science aficionados attempted to confront the fascinating question: What the elephant really is? One of such persons was Dr. W.H. Ale who felt an intriguing affinity to the elephant and realized that Ensa’s model corresponded to the first term in a multipole series for elephant’s mass distribution. Very soon he was able to formulate an advanced model by using multipoles up to the order of 300 and next 500, which also contained millions of parameters. He invented his own judicious fitting procedure, adjusted elephant’s multipole moments to data and obtained good results. He was even able to understand the physical origin of the so-called elephant jets and proved that they must originate from the rear end of the elephant. Based on his analyses, Ale was able to put forward a daring hypothesis that four large heavy appendices protrude from one side of the elephant. In support of that, he produced fuzzy 3D computer-generated images of elephant’s mass distribution. Despite its success, Ale’s work has not gained much appreciation within the broad community, which seemed to be emotionally attached to Ise’s conjecture. His work was promptly qualified as “ just fitting many parameters” , “ lacking physical understanding” , or outright “stupid” . Ale tried to argue that the elephant is a fairly complex object and, therefore, precise description of high-resolution experiments must involve many parameters. To no avail; when the directors of experimental facilities announced: “the elephant has been understood” , the Nobel Committee honored the achievement and work of Ise, Loppy, and Ensa (Ise promptly issued a statement saying that he finally does recall having formulated his conjecture). Ale died in solitude after many years of untreated depression. However, his model is still widely used in the Ale Research Center, named after him, which now studies other large mammals. This paper has been presented in guise of a summary talk during the Arctic FIDIPRO-EFES Workshop held in Saariselkä, Finland, on April 20-24, 2009, Future Prospects of Nuclear Structure Physics. The author gratefully acknowledges excellent working conditions at the Saariselkä Ski Center, where most of the work has been done.