Science, ethics and democracy

John Boyne’s novel, The boy in the striped pajamas (2007) is about the slaughter in the gas chamber in the Nazi concentration camps. The book ends thus:

Of course all this happened a long time ago and nothing like that could ever happen again.

Not in this day and age.

Is this true? Those things can never happen again?

I think this ending is not right. First, it’s not true that it all happened a long time ago. Seventy years is not a long time for historic events. Second, it’s not true that those things could never happen again. Have we forgotten the Ruanda massacres in the nineties?

But perhaps the author meant that those things can never happen again in Europe. Have we forgotten the Srebrenica massacre and the Sarajevo tragedy, also in the nineties?

Or perhaps he means that these things cannot happen in a democratic country. Has he forgotten that Hitler reached power after a democratic election? Has he forgotten that the Athenian democracy was discredited for millennia by their death sentence against Socrates, the result of a secret vote that took place just after the restoration of democracy, which followed the oligarchy imposed by Sparta after the Peloponnesian war?

Classifying living beings: Cladistics or complexity levels

The tree of life

Since Aristotle, living beings have been classified in kingdoms. At first there were two: plants, practically unmoving, and animals, capable of active movement.

When Antony van Leeuwenhoek discovered microorganisms, biologists tried to maintain this two-fold division, integrating some with animals (amoebas and Paramecium), others with plants (bacteria and microscopic algae and fungi). But at that level, the separation between animals and plants is blurry, and in the mid twentieth century a third kingdom was added to the other two: protists, unicellular living beings.

A little later, biologists came to the conclusion that the kingdom of plants should be divided into two: fungi at one side, all the other plats (metaphyta) at the other. By 1975, therefore, there were four different kingdoms.

Artificial life is not here

Saccharomyces cerevisiae (yeast)

Last spring, the media published the news that a scientific team had replaced the smallest chromosome of a yeast cell by a synthetic chromosome, built from the nucleic acid sequence of the replaced chromosome with a few changes, such as the elimination of a section. Once added to the yeast genome, the synthetic chromosome seemed to work correctly.

The headline of the article linked above is meaningful: Scientists Move Closer to Inventing Artificial Life. As it is worded, it seems to imply that we are close to building artificial life. But is this true? Or is this one of those typical overstatements of the media?

In the scientific parlance, artificial life may have two very different meanings:

The fine tuning problem

In two previous posts I dealt with the relation between the multiverse theories and the problem of fine tuning, noting that those theories do not solve the problem. This third post describes briefly what is the fine tuning problem.

Brandon Carter

In 1973 Brandon Carter formulated the anthropic principle, a name later deplored by its author, because it may be prone to misunderstandings. This principle is simply the verification that the universe must fulfill all the conditions necessary for our existence, since we are here.

Over a decade later, John Barrow and Frank Tipler published a book entitled The anthropic cosmological principle, which offered a stronger version of the anthropic principle, posing that the values of many of the universal constants are critical and minor variations would make life impossible. This finding raises the fine tuning problem, based on the analysis of the possible effects of changing the values of those constants. In other words, the universe seems designed to make life possible. Let’s look at a few examples:

Consequences of scientific fraud, a lesson for politicians

Scientific fraud is an important issue that can give rise to complex ethical problems. The mystery novel Gaudy night (1936), by Dorothy L. Sayers, offers a concrete example. When he is about to defend his doctoral thesis, a scientist discovers a little-known document that demolishes his work. Temptation is too strong, he steals the document and proceeds with his thesis. Unfortunately (for him) one of the university committee was aware of the existence of the document, tries to look it up and discovers that it is missing, and who was the last person who consulted it. The fraud is thus discovered, the thesis is rejected, the case is made public and the researcher is dismissed with unfavorable comments that put an end to his scientific career. As he must support a family, he has to accept a job below his level and finally commits suicide.

The characters in the novel formulate the following ethical problem: Must a person give up his vocation because of having yielded just once to a temptation of fraud? What comes first, the integrity of science or the fate and perhaps even the life of an individual human being? In the words of one of the characters: [That old piece of paper] made no difference to anybody. It wouldn’t have helped a single man or woman or child in the world - it wouldn’t have kept a cat alive; but you killed him for it.

The multiverse does not solve the fine tuning problem

Atheists use the multiverse theories to escape the need to accept God’s existence as the cause of a universe which seems to have been designed to make life possible (fine tuning). While they do this, they are contradicting one of their most beloved arguments against God’s existence, which they have been using since the nineteenth century. This one:

The theist hypothesis offers an explanation for the origin of the world based on two entities: God and the universe.

The atheist hypothesis only needs a single entity: the universe.

Ergo Occam’s razor favors the atheistic explanation.

As it is well known, the lex parsimoniae, also called Occam’s razor, one of the fundaments of the scientific method, asserts that, between two competitive theories, we must prefer that one with the fewest entities (or assumptions).

But the current situation is quite the opposite. The alternative to the theist hypothesis is no longer a single entity, the universe, but rather many (between 10⁵⁰⁰ and an infinity of universes). The previous argument must therefore be re-written thus:

The multiverse and the fine tuning problem

The multiverse theories appeared in cosmology over half a century ago, but they have proliferated and spread starting at the eighties, together with the discovery of the fine tuning problem, the verification that the universe appears to have been designed to make life and our existence possible: many of the physical parameters we consider independent adopt quite critical values, so that very small differences in those values would make the universe hostile to life.

The fine tuning problem has three possible solutions:

·         The universe has been designed by a creator.

·         Our existence is the result of a huge, incredible chance.

·         There are many universes and we are located in that one which is compatible with our existence (the multiverse hypothesis).

The probability of existence of extra-terrestrial intelligence

Normal statistical distribution.
The text makes reference to a uniform statistical distribution.

Probability is a well-known mathematical concept that was initially defined to quantify random data in mathematically known environments and has been extended to other situations.

For instance, the probability that the next car passing near me has a license plate with four identical figures is computed by dividing the number of favorable cases between the number of possible cases. The first number is ten: 0000, 1111, 2222, ... , 9999. The second is ten thousand: 0000, 0001, 0002, ... , 9998, 9999, in a uniform distribution. Therefore the indicated probability can be computed as one thousandth. Here we haven’t considered that vehicles can be removed from circulation, an independent random process that would not change significantly the result of the computation.

The problem is, sometimes we are interested in computing data in mathematically unknown environments. This can happen, for instance, when we ignore the number of favorable cases, or the number of possible cases, or both. In such situations, we can estimate the unknown data with more or less uncertainty. We speak then of a priori probability.

On-line bullying

In an article by the press agency Europa Press published on June 28 2012, which refers to a study performed by Microsoft among youths in the age range 8 to 17, it is stated that 37% of Spanish youths suffer on-line bullying through the Internet. This looks like a high figure, but it may depend on how bullying is defined.

Reading the article, it appears that 17 per cent of the polled declares having been addressed in an unfriendly way, 13 per cent have been targets of mockery and 19 per cent have felt insulted. Also, 24% of the youth confess that they bully other people.

Neither in the Europa Press article, nor in the summary of the Microsoft study, is there a definition of unfriendly behavior and the other forms of bullying. It appears that the youths who answered the poll just considered it thus.

Atheist arguments are still in the nineteenth century while theists have modernized

Interview with Manuel Alfonseca published in http://www.religionenlibertad.com/los-ateos-siguen-con-argumentos-del-siglo-xix-pero-los-teistas-38204.htm

Manuel Alfonseca was born in Madrid in 1946. He is the son of the painter and sculptor Manuel Alfonseca (Santana), is a doctor in Telecommunication Engineering and a Computer Scientist, has been a full professor, and is currently a honorary professor at the Universidad Autónoma of Madrid. 

His great gift is his ability to popularize science and express himself clearly, which has led him, not only to teaching and science, but also to the literary world (he has published fantasy, science fiction and historical novels). His work makes a bridge between "science" and "humanities", attested in his blog on popular science and his personal website. Now, in addition, he is one of the co-editors (along with Francisco-José Soler-Gil) of an unusual work for its breadth and ease of comprehension: 60 preguntas sobre ciencia y fe respondidas por 26 profesores de universidad (60 questions on science and faith answered by 26 professors). Without getting into the 60 questions, we shall try to explore the science-faith dialogue with a few questions, while strongly recommending the book to those who seek answers to the others.

Life expectancy and happiness

First, the news.

Headline: For sheep horns, biggest is not better

Source: Science News, 184:7, page 8, October 5, 2013.

Text: Sometimes it pays to be mediocre. A new study shows that sheep with a 50/50 blend of genes for small and big horns pass along more of their genes than their purely big-horned brethren, who mate more often... The results, published online August 21 in Nature, reveal that while biggerhorned sheep mated most successfully

each season, small-horned sheep survived longer... and mated more successfully than those with the smallest horns.

My comment:

The curse of Chalion

The Curse of Chalion: a fantasy novel based on Spanish history

Book cover

The Curse of Chalion, by Lois McMaster Bujold, is one of the best fantasy novels of the latest years. It belongs to that rare category, which also contains Tolkien's Lord of the Rings, C.S.Lewis's Perelandra, Walter M. Miller Jr.'s Canticle for Leibowitz, or Poul Anderson's Orbit unlimited, that combine an interesting adventure plot with important ethical dilemmas and deep questions about the nature of man and God.

In this novel, as deftly crafted as her Vorkosigan saga, Lois McMaster Bujold has pushed further the bounds of subcreation as defined by Tolkien in his paper On fairie stories. She presents us, not just a coherent imaginary universe, but even a strange God, which rather than three persons displays five, together with important differences from the God we have heard about.

The origin of life in other worlds

In a recent article published in the Annals of the National Academy of Sciences of the United States of America, Christopher McKay analyzes the requirements and limits for life in other worlds. Since we have no data at all about any concrete planet outside the Solar System, and very few about the planets and satellites in our system, apart from the Earth, the study focuses on the limits for life in our world and tries to extrapolate the results to the possible existence of extraterrestrial life.

Thus, for instance, he notices that on Earth there are extremophile organisms, able to survive in environments apparently hostile for life: between -15 and 122ºC; in conditions of extreme dryness; in an almost total absence of light (100.000 times less than the solar flux we use to receive); in the presence of ultraviolet rays and ionizing radiation...

What's the use of a child?

The importance of basic research

The secretary of the Royal Society of Sciences stood up and said:

“Mr. Faraday has the floor.”

“In today’s lecture, rather than speaking about a scientific subject, I’ll perform an experiment before your eyes. But first, allow me a short historical introduction. As you know, Oersted, Ampère and Arago proved that an electric current can give rise to magnetic phenomena. If you set a magnetic needle near an inactive copper wire, the needle points North. If a current passes through the wire, the needle deflects. If the wire is coiled and a current goes through it, the coil behaves as a magnet with two poles, North and South, the same as a typical ordinary magnet.

Scientists and religion

In 1914, psychologist James Henry Leuba surveyed 1,000 randomly selected scientists in the United States, asking them if they believed in a personal God, defined in this way: a God in intellectual and affective communication with man... to whom one may pray in the expectation of receiving an answer. Among those who answered the survey, 41.8% answered the question affirmatively, 41.5% negatively, the remainder did not know or refused to answer. From these data, Leuba drew the conclusion that faith in God would decrease with the advance of science, and predicted that by the late twentieth century virtually all scientists would be atheists.

In 1996, Larson and Witham repeated Leuba's survey using exactly the same question, so that the results were comparable. They found that 39.3% answered affirmatively, while 45.3% answered negatively. These numbers were therefore approximately the same as eighty years earlier. As the authors say in their paper, if in 1914 the high number of atheists was surprising, what was surprising in 1996 was the high number of believers.

These two surveys present a problem: Leuba and his followers consider atheists those who answered their question negatively. But who would answer negatively such a question? Not just atheists, also agnostics and indifferent, plus those who believe in a non-personal God.

Hallucinations

In a paper (Visions for all) published in its April 7th 2012 issue, Science News summarizes the work of Tanya Luhrmann about the God experiences that many people claim to have felt. After four years of research, the anthropologist believes that she has proved the surprising conclusion that normal people can have hallucinations. But since hallucinations are common in diseases like schizophrenia and psychosis, she predicts that people who have many of these experiences are likely to end up psychotic. In particular, the article says, it is possible that Joan of Arc would have become psychotic if the British had not burned her.

This argumentation has a hidden premise. If we make it explicit, the associated reasoning can be summarized as follows:

The precariousness of scientific theories

It is better to keep a certain skepticism about scientific theories,. Not only because these theories are always simple approximations tuned by further advances, as in the case of Newtonian gravitation and Einstein’s general relativity, quoted in a previous article. It may also be the case that a scientific theory, after decades, centuries or even millennia of total domination, turns out to be simply wrong. This has happened many times in all the sciences, as will be seen with a sample of a few selected cases.

·         In astronomy, Aristotle’s theory of quintessence, arguing that the heavenly bodies are not made of the same stuff as the Earth, was the standard theory for nearly two thousand years.

·         In mathematics, the problem of squaring the circle with ruler and compass wasted efforts for centuries until it was shown to have no solution. Although amateurs keep trying, at least professionals no longer have to waste their time with the alleged demonstration they regularly receive.

Lavoisier

·         In chemistry, the phlogiston theory, which dominated for nearly a century, tried to solve the problem of combustion assuming that a burning body loses a part of its substance (the mysterious phlogiston). The real process turned out to be precisely the opposite. Rather than losing phlogiston, burning bodies absorb oxygen, as Lavoisier showed in the late eighteenth century.

·         In physics, for almost half a century in the late nineteenth century, no one doubted the existence of the ether, a mysterious substance with strange properties, which should provide support for the movement of electromagnetic waves. In the early twentieth century it was concluded that the ether does not exist.

Cultural evolution and biological evolution

Cultural and biological evolution are similar because natural selection acts in both cases. Cultural productions compete against one another and many become extinct. As in the case of living beings, not always the best win. Chance has an influence. In this way, for instance, Windows-95 threw OS-2 out of the market, even though at that time the second operating system was better. Another example is the result of the war between the three competing models of video recording: Betamax, 2000 and VHS.

In the same way that living beings exhibit genetic variability (many varieties of the same gene co-existing in the same population), there is also a cultural variability, represented by the co-existence of old and new makes and models of the same product. At times of big change in the environment (we are just now experiencing one) a cultural product may escape extinction thanks to its variability, by combining versions and producing something new, better adapted to the new circumstances.

The parallel is quite impressive. What we call a species in the biological world, may be considered similar to a civilization. But there are also deep differences between both phenomena.

While studies about biological evolution get back in time to one century and a half ago, those about cultural evolution are more recent: not even half a century. One of its pioneers, Richard Dawkins (who invented the term meme for cultural elements equivalent to genes) made the mistake of considering biological and cultural evolution as identical processes, forgetting their differences. Cultural evolution is almost exclusively typical of man and exhibits new phenomena, emergent features that make it quite different from biological evolution:

Solution to the time machine problem

Answer to the problem posed in a previouspost, on August 18th 2014:

This is what happened in the second scenario: 

At 16:01, the original Max traveled to the future in the second time machine. When he arrived, he found there the second Max waiting for him with the first time machine. He moved to the other machine and traveled back to the past, arriving at 15:59. After changing machines again, he traveled to the future in the original time machine. He never returned.

Only these two scenarios are possible. Any other you may try to build would be inconsistent (try and you will see).

Consequences: 

It is easy to see that the world line for the machine is the same in both scenarios. What changes is the traveler’s world line.

1.            In scenario 1, the traveler does not change machines either in the present or in the future.

2.            In scenario 2, the traveler changes machines both in the present and in the future.

Therefore, if time travel to the past were possible, the traveler would not be free. What he does in the present logically determines what he must do in the future. If he changes machines now, he must change in the future. If he doesn’t, he mustn’t.

Conclusion: 

Nobody doubts that a human being is free to take an elementary decision such as changing chairs or not. 

Therefore time travel towards the past must be impossible.

Thematic thread on Time: Previous Next

Manuel Alfonseca

This is what science says about human life

With respect to current discussions about abortion, protection of life, and the rights of the pregnant woman, I think it timely to recall the scientific consensus about human life:

·        The life of every living being generated by means of sexual reproduction begins with the fertilization of the female by the male gamete, i.e. with the formation of the zygote. That is the point in time when a new being appears, of the same species as its parents, whose genetic endowment (its DNA) is different from that of its parents and any other living being of the same species, except for identical twins. This new living being will keep its genetic endowment until its death. This is the reason why the eggs of sea turtles and other endangered species are protected, because they are individuals of those species.

·        In every species of living beings who do not go through metamorphosis (including all reptiles, birds and mammals, and of course man) there is no sharp change in their development from the zygote to death. The different phases we use to make out (embryo, fetus, neonate, child, teenage, adult and old) are arbitrary, without any discontinuities. Not even the birth is anatomically discontinuous (it consists in cutting a blood vessel; physiologically it has other effects). There is no doubt that in all those phases, from the first to the last, the same individual is involved.

·        In every placental mammal (including man), the first phase of the life of the new individual takes place inside the body of the mother. Pregnancy is equivalent and replaces development inside the egg, which in reptiles and birds takes place outside the mother’s body. In both cases, maternity begins in fertilization, not in birth, whose equivalent is the rupture of the egg shell. A woman is a mother from the moment she becomes pregnant.

The time machine problem

I am posing here a problem with interesting consequences about the (im)possibility of time travel. I'll pose the problem by means of two science-fiction vignettes. If you decide to try your hand at solving it, you can describe your solution in a comment to this blog post. Next week I'll explain the solution and its consequences.

First vignette

At 15:55, Max told me:

“I have just invented a time machine. Do you want to see it?”

Of course, I accepted. 

• At 15:58, Max and I entered the room where the machine was. It looked like a simple metal chair. The machinery seemed to be located under the seat.
• At 15:59, while Max and I looked at the machine from the room’s door, a second exact copy of it suddenly appeared, just near the machine. In the second machine was seated an exact copy of Max. Amazed, Max and I looked at him.
• At 16:00, the original Max crossed the room, sat on the original machine, pressed a control and disappeared towards the future. The copy of Max, still sitting on the copy of the machine, observed attentively what he was doing.
• At 16:01, the copy of Max pressed a control in the copy of the machine and disappeared towards the future. Max and the machine never returned.

After thinking for some time, I deduced what had happened. At 16:00, Max travelled to the future in his time machine, but when he arrived he travelled back to the past, arriving at 15:59. He watched the original Max leaving on the original time machine at 16:00, went again to the future at 16:01 and never returned.

In the figure, the blue line represents Max, while the red broken line is the time machine.

Second vignette 

At 15:55, Max told me:

“I have just invented a time machine. Do you want to see it?”

Of course, I accepted. 

• At 15:58, Max and I entered the room where the machine was. It looked like a simple metal chair. The machinery seemed to be located under the seat.
• At 15:59, while Max and I looked at the machine from the room’s door, a second exact copy of it suddenly appeared, just near the machine. In the second machine was seated an exact copy of Max. Amazed, Max and I looked at him.
• At 16:00, the copy of Max stood up, went to the original machine, sat on it, pressed a control and disappeared towards the future. The original Max, near me, observed attentively what he was doing.
• At 16:01, the original Max crossed the room, sat on the copy of the machine, pressed a control and disappeared towards the future. Max and the machine never returned.

Please, kind reader, can you help me find out what had happened in this second scenario?

See solution
See Spanish version
Thematic thread on Time: Preceding Next

Manuel Alfonseca

The God Particle

Peter Higgs

With the discovery of Higgs boson, two years ago, the media and a few scientists have presented the discovery as the final completion of the standard theory of particle physics, in such a way that we now know everything and do not need God. Hence the nickname given to Higgs boson, the God particle, a name, by the way, that Higgs does not like.

The discovery of a particle whose existence was predicted nearly a half century ago is a spectacular success of the standard theory, comparable to the success achieved in 1846 by Newton’s theory of universal gravitation with the discovery of Neptune, whose existence had been predicted by Le Verrier and Adams. Then it was also said that we now know everything. 

Urbain Le Verrier

True, there was still a loose end, a very small discrepancy of just 43 seconds of arc per century in the precession of the orbit of Mercury. Le Verrier tried to repeat his success and predicted that this discrepancy was due to an unknown planet between Mercury and the Sun. He even gave it a name: Vulcan. For 60 years, many astronomers tried to find the mysterious planet in vain, for the problem in this case was in Newton’s theory, which eventually came to be just a first approximation of a new better theory that explained the discrepancy: Einstein's general relativity.

Could something similar happen to the standard theory of particle physics? Will its great success be followed by its first failure? Are there any loose ends still remaining in the theory?

The answer to the last question must be affirmative. The standard theory of particle physics has the following outstanding issues:

What is man?

Since about one century ago, after the consolidation of evolutionist theories, and getting from them philosophical consequences without a scientific basis, many biologists assert that man is an animal like any other, one between millions of species of living beings, and it would be impossible to set criteria to help us decide if one species is more advanced or more important than any other.

Is this true? I think it is evident that those criteria do exist, that we should not be denied the ability to compare and judge, two capabilities that have made our technological advances possible. I’ll mention just two of those criteria:

·         The origin of life, about 4000 million years ago, did not have an immediately observable impact on the physical aspect of the earth. Just a few changes in the water hue, or the apparition of cyanobacteria reefs. Nonetheless, the action of life on Earth continued slowly and culminated about 1000 million years ago in a new composition of the atmosphere with about 20 percent oxygen, which made respiration possible.

Multi-cellular living beings changed deeply the physical appearance of the Earth: the dominant color of continents turned green. Of the three kingdoms at this level of life, plant produced the largest impact, while fungi and animals are practically imperceptible from outer space.

In the last centuries, the situation has changed: for good or evil, the human species by itself has modified the aspect of our planet. The surface of the tropical forests is decreasing; many living species are in danger; holes in the ozonosphere turn up; the night sky is full of light; and, for the first time in history, the Earth has become an emitter of low frequency electromagnetic waves (radio and microwave), which makes our existence detectable by hypothetical extraterrestrial intelligences. A single species has done this in a terrifically short time, compared to the history of the Earth.

·         On the other hand, in very recent years, most members of the human species have become able to access a huge amount of information, an ever growing amount, over one quintillion bits (10¹⁸). Compare this figure with the information accessed by the members of any other species, from bacteria to chimpanzees: between one million and 200 million bits, seven to twelve orders of magnitude below ours. The information at our disposal may already be higher than the total amount of information accumulated by all the hundred million species of living beings considered to have existed from the origin of life, assuming that it makes sense to add it all together.

Is man a species like any other? No. For some biologists, biological classifications should give man at least the rank of a kingdom of nature, for it is very different to all the other species. Man was considered different during most of the history of mankind, until some biologists in the twentieth century started their continuous and surreptitious work of undermining human dignity.

Spanish version of this article
Thematic thread on What Is Man: Next

Manuel Alfonseca

The Dawkins Delusion

Richard Dawkins

This is my analysis of Richard Dawkins book, The God Delusion (2006). I'll start by signaling a couple of inconsistencies. There are many more, but detailing all would require a book size.

·         In chapter 3, Dawkins debunks the theistic argument of the admired religious scientists (how can you not believe in God, when so many admired scientists did believe?). I agree with him, this argument has no weight. But then, why does he use once and again the argument of the admired atheistic scientists? One half of chapter 1 is dedicated to tell us that Einstein did not believe in a personal God. In chapter 2 he asserts, more than once, that most of the founding fathers of the United States were atheists, although few of them dared to confess it publicly. (I suppose that's why they printed In God we trust in their paper currency). He also says that Thomas Huxley, who invented the word agnostic to classify himself, must have really been an atheist, although he never made it public, submitting to the demands of his time. He admits that Newton... did indeed claim to be religious. So did almost everybody [in his time]. A little more, and he would have also said that Newton was another hidden atheist.

The Grand Design

In 2010, the media gave a lot of coverage to a book on popular science by Stephen Hawking and L.Mlodinow, The Grand Design. I think it is time to make a few comments, which I am going to introduce by means of quotations of the book:

·         Philosophy is dead… Scientists have become the bearers of the torch of discovery in our quest for knowledge.

These words appear at the beginning of the first chapter. Although most of the book is just popular science, or history of science, it is ironical that the only original contribution (model-dependent realism) is purely philosophical.

·         Objective reality is unknowable, therefore we cannot assume it exists... Only the results of observations and the model we build to explain them exist... Every model is valid (real) in its own field of application... Two models with the same explaining power are equally valid... Ptolemy's model is as valid as Copernicus's... Their only difference is the fact that the second is simpler than the first.

The preceding text is not a literal quotation, but a summarized paraphrase of chapter 3, which describes model-dependent realism, the original contribution of the book (with Berkeley's permission). The authors forget that Copernicanism predicted correctly the stellar parallax, which cannot be explained in Ptolemy's. In the same chapter, Hawking and Mlodinow discard the steady state cosmological theory because it is unable to explain certain observations on the universe. Shouldn't they do the same with Ptolemy's?