Outer Limits of Reason (69 page)

22
. The literature is full of very passionate ideas about this topic. Somehow researchers “know” the answers to these questions. Unfortunately this humble writer simply does not “know” the answers.

23
. Many other topics in the philosophy of science impinge on the limitations of science. For example, philosophers discuss the existence of the laws of nature. To what extent are the laws real as opposed to being simply patterns of observations or socially constructed ideas? What are some of the practical limitations of science? To what extent is science influenced by the social structures of the scientists? See Rescher 1978 for more on the practical limitations of science. See Rescher 1999 for many other issues pertaining to the theoretical and philosophical limitations of science. There are many topics in classical epistemology that also have definite implications for the limitations of science. For example, philosophers ask how we can prove that we are not “brains in a vat” being fed stimuli. Another interesting philosophical thought is solipsism, the belief that one's mind is the only mind in existence. (Solipsists usually express shock that others do not accept their ideas.) Philosophers take this even further to “solipsism of the present moment,” which is the belief that one's mind is the only mind in existence and that existence only began five minutes ago. In other words, even one's memories are of recent origin. While these crazy ideas are clearly false, there are no logical or reason-based proofs to show that they are false. We leave such ideas for other writers.

24
. “La filosofia ´e scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si puo intendere se prima non s'impara a intender la lingua, e conoscer i caratteri, ne' quali ´e scritto. Egli´e scritto in lingua matematica, e i caratteri sono triangoli, cerchi, ed altre figure geometriche, senza i quali mezi e impossibile a intenderne umanamente parola; senza questi e un aggirarsi vanamente per un'oscuro laberinto” (Galileo Galilei,
Opere Il Saggiatore
, 171).

25
. Dirac 1963.

26
. Einstein 1921.

27
. Dirac 1982, 603.

28
. Dirac 1939, 122.

29
. Figure by Hadassah Yanofsky.

30
. Whewell 1858, vol. 1, 311.

31
. Einstein 1921.

32
. We will meet group theory in much more detail in sections
9.2
and
9.3
.

33
. Weinberg 1994, 157.

34
. Message of Pope Benedict XVI on the occasion of the international congress “From Galileo's Telescope to Evolutionary Cosmology: Science, Philosophy and Theology in Dialogue,” 2009,
http://www.vatican.va/holy_father/benedict_xvi/messages/pont-messages/2009/documents/hf_ben-xvi_mes_20091126_fisichella-telescopio_en.html
.

35
. Quoted in Bell 1937, 16.

36
. Gardner 2005.

37
. Even in physics, one can question the necessity of mathematics. Physics is about understanding causes and effects. Mathematics in physics is used to describe the exact
quantity
of causes and effects. My dissertation advisor, Alex Heller, reported a personal conversation with the great American physicist Richard Feynman, who said something along the lines of, “Physics is written in the language of mathematics. If we did not have mathematics, physics would not have progressed as much as it did and would be behind where it is now . . . by about fifteen minutes.” On the web, I found the following story: Feynman remarked in a lecture that “if all of mathematics disappeared, physics would be set back exactly one week.” The mathematician Mark Kac replied, “Precisely the week in which God created the world.”

38
. One might restrict the problems that sociology deals with and get phenomena suitable for contemporary mathematics. This is a central motivation of Rohit Parikh's social software project.

39
. Isaac Asimov's classic
Foundation
series is based on this idea.

40
. On the young physicist's boards are diagrams and equations of particle interactions. On the young mathematician's board are diagrams of objects with strange names like “cobordisms,” “cohomology,” and “homotopy functors.”

41
. Sidney Morgenbesser (1921–2004) is quoted as replying with this comment: “If there were nothing you'd still be complaining!” Woody Allen is quoted as saying, “What if everything is an illusion and nothing exists? In that case, I definitely overpaid for my carpet.”

42
. One can see the questions addressed in the last section as a further layer of these mysteries. Consider in particular the following question:

Question 4:  Why does this intelligence that is capable of understanding the structure of the universe use the language of mathematics to describe this structure?

Why is the language of mathematics so perfectly suited to describing the laws of physics? Permutations and combinations of mathematical operations that form equations and inequalities become the laws of nature. I dealt with this issue in the last section.

43
. Perhaps we are being a bit presumptuous in calling our species “intelligent.” After all, this species has waged numerous inane wars where millions of their own were slaughtered. As a whole, this species spends trillions of hours a year watching insipid television shows. And “intelligent” is not the right name for a species that invented spam e-mails and encourages narcissistic pastimes like Facebook. Nevertheless, over the millennia, this species produced many shining lights that make us worthy of the lofty title: Blaise Pascal, Isaac Newton, David Hume, Marie Curie, Albert Einstein, Arthur Stanley Eddington, Emmy Noether, Andrew Lloyd Webber, Meryl Streep, and, of course, tiramisu.

44
. In symbols, we can state this as [(A∨B)∧(∼B)]→A. This rule is a common part of logic and is called a
disjunctive syllogism.

45
. Freud was actually the first to point out this three-pronged attack on human beings in “A Difficulty in the Path of Psycho-Analysis” (1917).

46
. If we are to follow the participatory anthropic principle (which we will meet in a few pages), then conscious human observers are the actual
cause
of the universe being the way it is.

47
. One must separate two types of deities that are used for such explanations. There are the personal deities of revelation, who want to see the human drama unfold for whatever reasons. In contrast, there are the impersonal deities of the philosophers. Such deities neither reveal themselves nor demand anything of humans. These two types of deities should not be confused with each other. As Pascal famously wrote, “‘God of Abraham, God of Isaac, God of Jacob'—not of the philosophers and of the learned” (“DIEU d'Abraham, DIEU d'Isaac, DIEU de Jacob' non des philosophes et des savants”). In general, the impersonal god is equated with nature or perhaps “Nature.” A trendier New Age name would be something like “Cosmic Consciousness.” However, most philosophers and theologians who discuss the impersonal deity prefer the name “God” so as to invoke the awe and reverence historically associated with that title. It is very unclear how the existence of the impersonal deity answers any of the questions about why the universe is the way it is.

48
. J. D. Salinger describes the mother-in-law of a character in his fantastic novel
Raise High the Roof Beams, Carpenters
(2001) as follows: “A person deprived, for life, of any understanding or taste for the main current of poetry that flows through things, all things. She might as well be dead, and yet she goes on living, stopping off at delicatessens, seeing her analyst, consuming a novel every night, putting on her girdle, plotting for Muriel's health and prosperity. I love her. I find her unimaginably brave.” This character clearly does not care about the implications of a fine-tuned universe or the anthropic principle.

49
. Some people use the fact that the universe is not propitious for intelligent life to explain the
Fermi paradox
. This paradox asks why no intelligent beings from the billions of stars within each of the billions of galaxies have visited us (other than for some short visits in the episodes of the
X-Files
). There are many suggested answers to this mystery. In 2002, Stephen Webb published a book titled
If the Universe Is Teeming with Aliens . . . Where Is Everybody? Fifty Solutions to Fermi's Paradox and the Problem of Extraterrestrial Life
. The fiftieth solution—and the one Webb prefers—is that this universe did not generate other intelligent life forms and we are all alone. The first solution in the book, reportedly given by the physicist Leó Szilárd, is that “they are already here among us: they just call themselves Hungarians.” See Webb 2002, 28.

50
. Perhaps we can say that the universe is against having intelligent life and that the chances of having intelligent life are, say, 0.0000001 percent. We, therefore, only see intelligent life in 0.0000001 percent of the universe.

51
. There is a bit of controversy in the literature about the veracity of this discovery. Originally it was thought that these life forms live off arsenic. It is now believed that they only live in arsenic. I am grateful to Jolly Mathen for pointing this out.

52
. See Weinberg 1994, 221.

53
. In fact, most authors do not take this as a multiverse theory.

54
. Eye of Rivka Yanofsky. Figure by Hadassah Yanofsky.

55
. Warning: long-term concentration about combining the participatory anthropic principle and the delayed-choice quantum eraser experiment can cause feelings of mysticism and madness.

56
. A proponent of a multiverse theory might contend that at some point we must stop asking questions. They would say we are permitted to ask about a universe and its properties but we are not permitted to ask why the multiverse has the structure it has. Such questions would get us into an infinite regression or are nonsense. This argument is a page out of the playbook of medieval theologians who argued that everything must have a cause and the cause of the universe is a deity; however, one is not permitted to inquire about the cause of the deity. Such restrictions on permitted questions are unappealing. As long as we have intelligence, we must go on asking questions.

57
. Manson 2003, 18.

58
. Eddington 1939, 21.

59
. Eddington 1958, 16.

60
. We will meet these questions again in 
section 10.3
.

61
. Dyson 1979, 250. 

Chapter 9

1
. Gibbon 2001, 142.

2
. Churchill 1996, 27.

3
. Allen 1993, 62.

4
. The difference between rational numbers and irrational numbers is not only a topic for ancient Greek philosophy and religion. We can have a similar discussion today. We imagine the world is somehow described and governed by real (and complex) numbers. The table is 5.82252932 . . . feet long; the temperature is 67.19153228 . . . . degrees Fahrenheit; the time it will take for the ball to land is 5.83245 . . . seconds. However, the human mind cannot retain an arbitrary real (or complex) number. Our brains are finite machines and can only deal with whole numbers or the ratio of two whole numbers (i.e., rational numbers). Similarly computers are limited in the types of numbers they can hold. This disparity between the “real world” and what we can know about the “real world” is a genuine limitation of reason.

There are at least two ways of getting around this limitation. First, we can say that the real world is discrete and thus suitable for rational numbers. As we have seen, quantum mechanics (
section 7.2
) and the wisdom of Zeno (
section 3.2
) assure us that the universe is discrete and that there is no information beyond Plank's length, Plank's energy, and Plank's time. Thus rational numbers are all that is needed to describe and understand the “real world.” Another way of bridging this separation between the human/computer capacity and the “real world” is to realize that although we cannot hold arbitrary real numbers in our minds, we nevertheless deal with them. I cannot hold all the digits of pi and
e
in my head, but I can describe these numbers perfectly. Pi is simply the ratio of the circumference of a perfect circle (something that only exists in the mind, not in the real world) to its diameter. Besides, to describe arbitrary real numbers, I have ways of generating as many digits as I need. In that sense, there is a way of describing real numbers. I am certain the final opinions on this topic have not been uttered.

5
. One can almost see Euclid's first four axioms of geometry (see 
section 8.2
) from these two constructions.

6
. “Tu prieras publiquement Jacobi ou Gauss de donner leur avis, non sur la vérité, mais sur l'importance des théorèmes. Après cela, il y aura, j'espere, des gens qui trouveront leur profit à déchiffrer tout ce gâchis.”

7
. “Ne pleure pas, Alfred! J'ai besoin de tout mon courage pour mourir à vingt ans.”

8
. Weyl 1952, 138.

9
. We met this genius in the
chapter 8
. He invented complex numbers and was also one of the founders of probability theory. Despite a terribly tragic life he nevertheless made tremendous accomplishments. See section 5.5 of Penrose 1994.

10
. Just for fun, here is one of the formulas used to find a solution: