Science « can’t see the forest

Archive for Science

Not such a bright guy? Neither are his little guys.

Posted in Biology, Genetics, Science, health, medicine, men, men's health, reproduction, research, science news, sex with tags Biology, Genetics, health, medicine, men, men's health, reproduction, research, Science, science news, sex on 12/6/08 by Curtis

| | | | | | | |

spermies Okay, that’s taking it a little too far. But a study from the UK Institute of Psychiatry published in the journal Intelligence claims to have found direct correlations between a man’s mental aptitude and the cleverness of his sperm.

Working with data from 425 U.S. servicemen in the Vietnam War, the research team found that, “independently of age and lifestyle, intelligence was correlated with all three measures of sperm quality - numbers, concentration, and ability to move.”

ivy_league_pennants_3480big Other than making themselves feel better, the scientists are interested in the genetics of intelligence and how they might be related to other measures of fitness and health, such as sperminess. While the statistical links found are small, the researchers say they are valid and telling and cannot be the result of lifestyle factors; it’s not going to make a great difference in their ability to conceive, but men of above-average intelligence definitely tend to produce above-average sperm, the study says.

From BBC News:

Lead researcher Dr Rosalind Arden said: “This does not mean that men who prefer Play-Doh to Plato always have poor sperm: the relationship we found was marginal.

“But our results do support the theoretically important ‘fitness factor’ idea.

“We look forward to seeing if the results can be replicated in other data sets, with other measures of intelligence and other measures of physical health that are also strongly related to evolutionary fitness.”

Dr Allan Pacey is an expert in fertility at the University of Sheffield.

He said: “The fact that it’s possible to detect a statistical relationship between intelligence and semen quality in adult men probably says more about the co-development of brain and testicles when the man was in his mother’s womb, and therefore how well they both function in adult life, rather than suggesting that playing Sudoku can somehow stimulate more sperm to be produced.

“The improvement in semen quality with intelligence observed in this paper is small and therefore it is unlikely to have a big impact on the ability of men of different intelligences to conceive.”

Leave A Comment »

Implant Works to ‘Read Man’s Thoughts’

Posted in Science, brain, computers, medicine, neurology, technology with tags brain, computers, medicine, neurology, Science, technology on 11/30/07 by Curtis

| | | | | | | |

For eight years, Eric Ramsay has been ‘locked in.’ Since a terrible car crash, Ramsay has been conscious but almost completely paralyzed and unable to communicate with the world around him except through eye movements.

But neuroscientists from Boston University, according to Communist Robot, have implanted an electrode in Ramsay’s brain which, they say, currently allows them to correctly record the sounds Ramsay is imagining about 80% of the time. That is, the patient merely thinks the words he would like to say, and the electrochemical signals recorded by the device are interpreted by the researchers. The implant monitors the activity of about 41 neurons located in an area of the brain which is responsible for generating speech (perhaps Broca’s area? Just an editorial guess).

Soon, the electrode will output to a computer which will play the interpreted sounds back to Ramsay in real time, allowing him to more precisely calibrate the device to the speech he is imagining.

Leave A Comment »

Exponents, Logarithms, and the Number e

Posted in Education, Science, algebra, mathematics, numbers with tags algebra, Education, mathematics, numbers, Science on 11/25/07 by Curtis

| | | | | | | |

Mathematics was never one of my academic strengths. Blog admin isn’t a headline on my résumé, either. In college, though, I’ve found myself to be far less averse to the numerical arts than in high school, a change of attitude I chalk up to better teachers and to my own growing curiosity in fields such as cosmology, linguistics, analytic philosophy, and the like. I’m still in no danger of becoming a mathematician, I assure you; consequently, the part of the post wherein I actually know what I’m talking about probably ends with this period.

This term, the prof took us on a scenic, leisurely tour of linear and quadratic equations. When we arrived in the country of exponential and logarithmic functions, however, he quickened his pace severely and proceeded to administer the most grueling, extensive exam of the term thusfar. Naturally, necessarily, I was moved to investigate the material on my own. I am sharing some of my findings in hopes that they may prove interesting and useful to other beginning and intermediate students of mathematics. This is not to mention providing a platform for the more algebraically inclined to prove what a dunce I am. Be kind, I prithee, for sooth.

Contents

Exponents and Rules for Exponentiation

Just as multiplication is a shortcut for repetitive addition, so exponentiation is a shortcut for repetitive multiplication. We know that $2 \cdot 5 = 2 + 2 + 2 + 2 + 2 = 10$ ; similarly, $2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32$ . We read the multiplication as “2 times 5,” and each of these two numbers we call the factors of the resulting product, which is 10. The exponentiation we might read as “2 to the fifth power,” or simply “2 to the fifth,” where 2 is the base, the number being operated on, and 5 is the exponent. An exponent essentially tells us how many copies of the base to multiply to complete the operation. So, $3^2 = 3 \cdot 3 = 9$ , and $3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81$ .

There are certain rules for exponentiation, or properties of exponents, if you will, which give them their usefulness as a shortcut to multiplying large sums. Dealing with expressions and equations involving exponents is made much easier if one masters these few concepts from the outset:

$a^m \cdot a^n = a^{(m+n)}$ . That is, if we multiply a base to one power times the same base to another power, the product is equal to our base to the power of the sum of the two exponents. For example, $2^2 \cdot 2^3 = 2^5$ , which is 32. Conversely, we know that we could rewrite $2^5$ as $2^1 \cdot 2^4$ , in addition to $2^2 \cdot 2^3$ , since the sum of the exponents is 5 in both cases.
$a^m / a^n = a^{(m-n)}$ . Similarly, dividing a base to one power by the same base to another power gives a quotient equal to the given base to the power of the difference of the two exponents. $2^5 / 2^2 = 2^3$ , or $32 / 4 = 8$ .
$(a^m)^n = a^{(mn)}$ . If we raise a base to a power and then, in turn, raise that product to another power, the end product is equal to our base to the power of the product of the two exponents. For example, $2^6 = {(2^2)}^3$ , or $64 = 4^3$ .

Special cases and notes on terminology with which to be familiar include:

Exponents 1 and 0. Any base raised to the first power is that number itself, so $2^1 = 2$ , and $1449^1 = 1449$ . Any base raised to the 0 power (even base 0, by most interpretations) equals 1, so $2^0 = 1$ , and $1449^0 = 1$ as well. This is because, according to our rule (1) above, we know, for example, that $3^3 = 3^2 \cdot 3^1$ , or $27 = 9 \cdot 3$ . Following the same principle, we see that $3^1 = 3^1 \cdot 3^0$ , since the sum of the exponents 1 and 0 is 1 and since $3^1 = 3$ ; the quantity $3^0$ , then, must equal 1, and indeed any number to the 0 power must be 1 for the same reason.
Exponents 2 and 3. The common terminology for $x^2$ is “x squared,” and $x^3$ is read as “x cubed.” This is because of geometry; if we take the length of the side of a square as our base and raise it to the second power, the result is the area of the square in square units. Similarly, the length of the side of a cube raised to the third power gives the volume of the cube in cubic units.

Negative and Fractional Bases

What happens if our base is a negative number, assuming we raise it to a positive, whole exponent?

$(-x)^n$ , where n is an even number, produces $x^n$ . That is, $-4^2 = 16$ , and $-5^4 = 625$ . This is because $-n \cdot -n = +n^2$ ; the negatives cancel after one multiplication.
$(-x)^n$ , where n is an odd number, produces $-x^n$ . So $-2^3 = -8$ , and $-3^3 = -27$ . This is because $-n \cdot -n = +n^2$ , but that positive product times -n once more gives $-n^3$ , since a positive number times a negative number yields a negative product.

Please note that $(-x)^n$ is not the same as $-x^n$ ! The first generally denotes -x to some power; the second, which also could be written as $-(x^n)$ , asks for the opposite of the quantity “x to some power.” For example, $(-3)^2 = 9$ , but $-(3^2) = -9$ . The placement of parentheses determines the order of operations in such examples. When no parentheses are present, the principle that $x^n$ denotes a single quantity in unsimplified form means that the negative sign is meant to apply to that quantity after it has been simplified.

There is no special rule to consider, really, when the base is fractional—the results just look a bit different, since we are essentially multiplying fractions. Consider $(\frac{1}{4})^2 = \frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}$ , or $(- \frac{2}{3})^3 = - \frac{2}{3} \cdot - \frac{2}{3} \cdot - \frac{2}{3} = - \frac{8}{27}$ .

Negative and Fractional Exponents

Now the soup thickens a bit.

$x^{-n} = \frac{1}{x^n}$ . In other words, a base raised to a negative power gives the reciprocal of that base, or 1 over that number. So, $2^{-2} = \frac{1}{2^2} = \frac{1}{4}$ .
$x^\frac{m}{n} = \sqrt[n]{x^m}$ . The procedure for fractional exponents is perhaps more precarious to describe than to use in practice. Suppose we are asked to evaluate $4^{\frac{1}{2}}$ . Using our rule formula, we would get $\sqrt[2]{4^1}$ , which simplifies to 2, since any number to the first power is that number itself and since we know the square root of 4 to be 2. Note that the 2 outside the radical sign is superfluous, since we understand a radical alone to mean “square root;” we added it just for clarity in correspondence with our formula. For an example in which the numerator of the exponent is not 1, consider $\large 2^\frac{2}{5}$ . Again, following our rule formula, we get $\sqrt[5]{2^2}$ , which, since we know that 2 squared is 4, would simplify to the fifth root of four, $\sqrt[5]{4}$ .

In terms of dealing with rule (2) in practice, the helpful verbal phrase to know is that “x to the m over n power equals the nth root of x to the m power.” A bit unwieldy, yes; but after a bit of practice it begins to come naturally.

A Visual Perspective on Exponentiation

exponential functions2

In this graph, the dark blue line is the graph of $y = x^2$ . You can see that, right where it exits the picture to the north, $x = 2$ or $-2$ and $y = 4$ . The two other graphs that are also parabolic in shape (U-shaped) are those of $y = x^4$ (red) and $y = x^8$ (green). Notice that, the higher the exponent, the steeper the parabola becomes, for obvious reasons.

There are three other graphs in the picture which appear to rise from near the origin (0,0) and fly off to the right; these are the graphs of $y = x^\frac{1}{2}$ , $y = x^\frac{1}{4}$ , and $y = x^\frac{1}{8}$ . Because $x^\frac{m}{n} = \sqrt[n]{x^m}$ , these graphs are equivalent to root functions—that is, they are the same as $y = \sqrt{x}$ , $y = \sqrt[4]{x}$ , and $y = \sqrt[8]{x}$ . The graphs of the even-numbered root functions are shaped like halves of sideways parabolas; the odd-numbered root functions, which include negative y values, are shaped differently.

Note that every graph passes through the point (1,1). This is because 1 raised to any power remains 1. Neat, huh? Well, at any rate, I think so. ;-)

Logarithms in General, and Their Properties

What is a logarithm? We said earlier that, in exponential operations, there is a base, which is the number being operated upon, and an exponent, which tells us how many copies of the base to multiply. Such an exponential expression is the antilogarithm of a logarithmic function of the same base. We know, for instance, that $2^5 = 32$ . But what if we were asked the question: to what power must we raise the base 2 to get a product of 32?

In mathspeak, this is written: $x = \log_2(32)$ . We know the answer is 5, since $2^5 = 32$ .The logarithm of a number, then, is the power to which we must raise a given base in order to obtain that number. The subscript number gives us the base, and the other quantity is the number of which we are finding the logarithm. So, for example, $\log_{10}(100) = 2$ , since $10^2 = 100$ ; and $\log_3(81) = 4$ , since $3^4 = 81$ .

The equation set which defines this identity of logarithms can be written as:

$x = log_b(y)$

$b^x = y$

We can see that, just as division can be used to “undo” multiplication for a given factor, so logarithms can “undo” exponential operations upon a given base. Note that it is not possible to find the real logarithm of a negative number, because the logarithm is, in effect, the value of an exponent. For example, while $\log_{-3}(9) = 2$ , because $(-3)^2 = 9$ , it is the base which is negative, not 9. The quantity $\log_3(-9)$ is undefined by real numbers; there is no power to which 3 can be raised to give a product of -9 (although there is an imaginary power—let’s not go there right now!).

There are some general properties of logarithms which make them useful tools in complex calculations:

$\log_b(y^a) = a \log_b(y)$ . So, then, for $\log_{10}(10^3)$ , we can create the equivalence $3 \log_{10}(10)$ . That is, the base-10 logarithm of 1000 is the same as 3 times the base-10 logarithm of 10. It checks: $10^1 = 10$ , and $10^3 = 1000$ .
$\log_b(b^a) = a$ . This seems self-evident enough. For $\log_{10}(100)$ , the answer is, of course, 2, because $10^2 = 100$ .
$\log_b(ac) = \log_b(a) + \log_b(c)$ . This is an expansion of a logarithm. Consider $\log_2(32)$ . We know that $32 = 4 \cdot 8$ , so this rule dictates that $\log_2(32) = \log_2(4) + \log_2(8)$ , or $5 = 2 + 3$ .
$\log_b(\frac{a}{c}) = \log_b(a) - \log_b(c)$ . Here we have the sister of rule (3). We can rewrite 4 as $\frac{32}{8}$ , and then can see that $\log_2(32) - \log_2(8) = \log_2(4)$ , or $5 - 3 = 2$ .

Another special rule, the “change of base” rule, is formulated as

$\log_b(a) = \frac{\log_d(a)}{\log_d(b)}$

where d and b represent different bases. For an example,

$\log_2(32) = \frac{\log_{10}(32)}{\log_{10}(2)}$ , or

$5 = \frac{1.50515}{0.30103}$ , approximately. This rule can be used to convert from one base to another, such as when trying to find, say, base-5 logarithms with a calculator that handles only bases e and 10.

Some Uses of Logarithms

test tubes

Logarithms were an important tool in speeding up meticulous multiplications in the days before computers entered the scene, an application most often credited to the designs of John Napier (1550 - 1617). Volumes which consisted of tables of logarithms and antilogarithms were published, so that, to multiply two quantities, the logarithms of each could be looked up and added together. In turn, the antilogarithm of the sum of these logarithms could be looked up, yielding the desired product of the original factors.

Logarithmic scales are important in numerous applications of science. pH, for example, the measure of chemical acidity or alkalinity, can be defined as:

$\mbox{pH} \approx -\log_{10}{\frac{[\mathrm{H^+}]}{1~\mathrm{mol/L}}}$

That is, the pH of a substance is the negative base-10 logarithm of the concentration of hydrogen ions in that substance, measured in moles per liter. Because pH is plotted along a base-10 logarithmic scale, a substance with pH 8 is 10 times as alkaline as a neutral substance (pH 7), and a substance with pH 5 would be 100 times as acidic as the same neutral substance (the lower the pH, the more acidic the substance; higher pH indicates alkalinity).

The Richter Scale for measuring seismic activity is also base-10 logarithmic; thus an earthquake which measures 4.0 produces a seismograph wave of an amplitude that is 10 times as great as the wave produced by a 3.0 quake; but the actual seismic energy represented by those graph measurements is logarithmic to approximately base-32, so that the energy released by a 4.0 quake is not ten times, but about 32 times, that created by a 3.0 quake.

Logarithms are also of interest because they are capable of mapping the set of positive real numbers (under multiplication) to the set of all real numbers (under addition). In so doing, they describe an isomorphic relationship. Consider that $\log_(n) > 0$ if $n > 1$ , and that $\log_(n) < 0$ if $n < 1$ . That is, while we cannot take the real logarithm of a negative number, the logarithm of a positive number greater than 0 but less than 1 will be a unique negative number, while the logarithms of all numbers greater than 1 are unique positive numbers. This kind of 1:1 mapping is called a bijection.

Notes on Notation and Nomenclature

How logarithmic expressions are notated depends heavily upon context, as there are no universally agreed-upon conventions. Most modern calculators use log to mean ‘base-10 log’ and ln to mean ‘natural log’ (we will discuss the natural logarithm presently), a convention followed by many engineers.

Because our system of mathematics is normally executed in base-10, owing to the number of fingers of the average human, base-10 logarithms are frequently referred to as “common logarithms.” However, some mathematicians take log to mean ‘natural logarithm’ rather than “base-10 logarithm,” and do not use the ln expression at all. Also, computer technicians sometimes take log to mean “base-2 logarithm” since they deal with binary (base-2) numbers so often.

Suffice it to say, it is best to specify the base of a logarithm if there is a chance of misinterpretation. In most modern mathematics textbooks, the engineering conventions are followed, so that $\log(12)$ means the “base-10 logarithm of 12,” while $\ln(12)$ means the “natural logarithm of 12.”

The number e

$e \approx 2.71828182846$

The mathematical constant e, sometimes called Euler’s number, is a transcendental, irrational number (a non-terminating, non-repeating decimal) with remarkable properties. Specifically, it is the base of the natural logarithm, approximated to three decimal places by the number 2.718.

What is so special about this number? Nothing overtly obvious, perhaps, but e is one of the most important numbers in mathematics, right up there with stars like 0, 1, pi, and phi.

In this graph, the thick, black diagonal line is the graph of $y = x + 1$ , a line of slope 1 which passes through the point (0,1).

The three colored lines represent three exponential functions. The red line is the graph of $y = 3^x$ , the green is $y = 2^x$ ; and, in between these values, sits the thicker blue line, which is the graph of $y = e^x$ , or approximately $2.718^x$ .

E is the only number n such that the derivative of $n^x$ (the derivative is the tangent line—the black line above) has the y-intercept of exactly (0,1) and is there exactly tangent to the curve. Both $2^x$ and $3^x$ slightly miss the mark, but $e^x$ , which is somewhere between them, is precisely tangent to the line $y = x + 1$ as it crosses the y axis.

Jacob Bernoulli (1654 - 1705) may have been the first to discover some of the more remarkable characteristics of e. He discovered its identity (approximately, of course) by studying a problem on compound interest.

Suppose we were to open an interest-bearing account in the amount of $1.00, which happened to pay the remarkable dividend of 100% interest per year. If the interest were compounded only annually, then the value of the account at the end of the year would be $2.00. If the interest were compounded twice annually, though, we would be credited $1.00 times $1.5^2$ , or $2.25, at the end of the year. If it were compounded quarterly, it would be worth about $2.44 at year’s end; compounding daily—that is, compounding 365 times—would put the value at $2.71 after 12 months.

Bernoulli noticed that, as the number of compoundings increased, the extra revenue produced by additional compoundings diminished. That is, while 4 compoundings would produce revenues $0.44 greater than a single compounding, a whopping 365 compoundings would add just $0.27 more revenue than what could be earned with only 4 compoundings.

Noting this trend, Bernoulli calculated that e is the value of the account if the interest is compounded an infinite number of times. The more compoundings, the closer the value of an account with a principal amount of $1.00 at an interest rate of 100% approaches approximately $2.7182818. . .you get the picture.

The following sequence illustrates this progression, and can be tested on a scientific calculator:

$(1 + \frac{1}{10})^{10} = (1.1)^{10} \approx 2.5937$
$(1 + \frac{1}{100})^{100} = (1.01)^{100} \approx 2.7048$
$(1 + \frac{1}{1000})^{1000} = (1.001)^{1000} \approx 2.717$
$(1 + \frac{1}{10000})^{10000} = (1.0001)^{10000} \approx 2.7181$

The larger n becomes, the closer the value of $(1 + \frac{1}{n})^n$ approaches e. E is the limit of this expression as n approaches infinity.

Another related and perhaps even more interesting way to define e is as the sum of the infinite series:

$\frac {1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \frac{1}{6!} \cdots$

! is the factorial symbol. The factorial of a number is the product of all positive integers which are less than or equal to that number. $O! = 1$ because the product of no numbers at all is 1; 1 is the “empty product” in number theory. $2! = 2 \cdot 1 = 2$ , $3! = 3 \cdot 2 \cdot 1 = 6$ , and $4! = 4 \cdot 3 \cdot 2 \cdot 1 = 24$ , etc. The further we expand the series, the closer the sum of the reciprocals approaches e. If we stop at 10!, we get

$\frac {1}{1} + \frac{1}{1} + \frac{1}{2} + \frac{1}{6} + \frac{1}{24} + \frac {1}{120} + \frac {1}{720} + \frac{1}{5040} + \frac{1}{40320} + \frac{1}{362880} + \frac{1}{3628800} \approx 2.71828$

We are already mindbendingly close to e by tossing in the towel at just $\frac{1}{10!}$ , but we could continue far past $\frac{1}{1000000000000!}$ , and thereby only slightly more accurately approximate its value.

Such is the magic of e, and why it is one of the most beautiful numbers we know.

Natural logarithms

Natural logarithms are defined as logarithms to the base e, and are most frequently represented by the expression $\ln(x)$ . So, then, the equation $x = \ln(1)$ effectively asks us: to what power must we raise e to obtain the product 1? The answer in this case happens to be 0, since any number to the 0 power is 1.

The following graph shows $y = \log_{10}(x)$ (blue) and $y = \ln(x)$ (red), for comparison.

log functions

Note that, on the blue graph, $x = 10$ where $y = 1$ because $\log_{10}(10) = 1$ ; on the red graph, $x \approx 2.718$ where $y = 1$ because $\ln(e) = 1$ . Both graphs pass through the point (1,0) because, since any number to the 0 power is 1, the logarithm of 1 is 0 in every base.

A Basic Example of Logarithms in Algebra

In rudimentary algebra, one immediately useful feature of logarithms is to help find the identity of a variable which is an exponent or part of an exponent by “undoing” the exponentiation.Consider the equation $2^{3x} = 10$ . How do we find x?Recall the property for logarithms we listed above which states that $\log_b(y^a) = a \log_b(y)$ . This means that $2^{3x} = 3x\log(2)$ . We will use base-10 since it is convenient for computers and calculators; we could, in theory, use any base for a calculation such as this, including, of course e.

The rules of algebra dictate that what is done to one side of the equation must be done to the other; observing this, we get $3x\log(2) = \log(10)$ . We then divide through by $\log(2)$ , yielding $3x = \frac{\log(10)}{\log(2)}$ . Now we can divide through again, this time by three, giving us the exact answer:

$x = \frac{\frac{\log(10)}{\log(2)}}{3}$ .

If we use a calculator to approximate the base-10 logarithmic values (log button) and perform the arithmetic, we see that $x \approx 1.107$ . Plugging that value back into the original equation to check our work, we see that $2^{(3 \cdot 1.107)} \approx 10$ .

Further reading

Wikipedia - Exponentiation

Wikipedia - Logarithms

Wikipedia - The Number E

8 Comments »

Schizophrenia: An Unpleasant Side Effect of Natural Selection?

Posted in Biology, Science, evolution, medicine, mental illness, natural selection, neurology, schizophrenia with tags Biology, evolution, medicine, mental illness, natural selection, neurology, schizophrenia, Science on 11/23/07 by Curtis

| | | | | | | |

bluebrain Recent studies indicate that schizophrenic conditions may stem from a genetically-triggered maladaptation involving the gene DISC1, which, according to research, has been selected for in evolution even though it contributes to schizophrenia. Compare this with sickle-cell anemia: it is caused by having two mutated copies of a certain gene, while those with just one copy of the mutation are naturally protected against malaria.

Discover Online reports:

One of the key tenets of Darwinism is that adaptations that work against the survival of a species are destined to disappear. So why does schizophrenia continue to linger on? Could it be that it confers some advantage?

For years, scientists struggled to identify an adaptive advantage that might explain schizophrenia’s persistence. Researchers from various disciplines volleyed ideas back and forth. Some argued that the genes implicated in the disease promoted creativity; others believed that schizophrenics were frustrated cult leaders—unorthodox thinkers constitutionally “engineered” to lead segments of humanity to break off from the herd, but who lacked the charisma to effect much change. None of the theories gained much traction.

New research is pointing to a different possibility: There may be no adaptive advantage provided by schizophrenia in and of itself, but rather from some genes that contribute to the disease. According to a study published in the Proceedings of the Royal Society, there is evidence that some of the gene variants associated with schizophrenia—especially a mutation in a gene called disrupted-in-schizophrenia 1 (DISC1)—have been selected for by evolution. This supports the idea that the disease may be a maladaptive combination of mutations that individually have the potential to enhance fitness. It could be a more complicated version of the familiar case of sickle cell anemia: having two mutant copies of a certain gene causes the disease, whereas having only one mutant copy provides protection against malaria.

A recent study headed up by Johns Hopkins University neuroscientists may have found what kind of process goes awry in schizophrenic brains. Researchers found that DISC1 regulates the migration of new neurons in the adult brain. When the levels of DISC1 were reduced in mice during adult neurogenesis, the newborn neurons sped up and overshot their intended targets within the hippocampus, says Xin Duan, a study collaborator. When the neurons finally reached their destinations, they forged an unusual number of connections with neighboring cells, a series of events that might give rise to the abnormal—and quite crippling—brain functions associated with schizophrenia, according to Hongjun Song, a Johns Hopkins neurologist who also worked on the study. It is possible, Song says, that further research will lead to a drug that treats schizophrenia by restoring normal neurogenesis.

So what evolutionary advantage could schizophrenia-related genes bring to people who have some of the genes but not the disease? For now, this remains one of the many open questions about this puzzling condition.

Leave A Comment »

The Chutzpah of Intelligent Design

Posted in Propaganda, Religion, Science, evolution, faith, intelligent design with tags evolution, faith, intelligent design, Propaganda, Religion, Science on 11/22/07 by Curtis

| | | | | | | |

From the lively Jewcy comes mathematics professor Jason Rosenhouse’s response to an exchange between writer Neal Pollak and Discovery Institute senior fellow David Klinghoffer:

I do not know what you do for a living, but I suspect you are pretty good at it. You probably trained for years to learn the basic elements of your craft, and then honed those skills through more years of on-the-job experience. Now imagine that someone without that training and experience presumes to discourse on your profession. Worse, they make assertions and arguments that are obvious nonsense to anyone versed in the subject. Not an altogether uncommon experience for you, I suspect, but one that is no less annoying for that. . .

. . .

Creationists of all stripes, be they the old-school Bible thumpers or the slightly more sophisticated ID proponents, do very well in public debates and scripted presentations. Any venue, in fact, in which flash and performance art are the main features. But place them in an environment where evidence and logic reign, such as a scientific conference or a courtroom trial, and suddenly they are far less impressive. Why do you suppose that is?

Let us be blunt. The specific scientific claims of ID proponents have been decisively refuted over and over again. Their sleazy use of rhetoric and propaganda has shown they have little interest in open and honest debate. They take quotations out of context, distort evidence, misrepresent whole scientific disciplines, oversimplify difficult ideas, and impugn the integrity of scientists. All the while they claim God’s blessing for their project and invoke conspiracy theories against those who disagree. And when they are done with all that, then they turn around and accuse scientists of being arrogant.

Where I come from we call that chutzpah.

Yes, that certainly just about sums it up.

Leave A Comment »

55 Cancri - A Home Away from Home?

Posted in SETI, Science, astronomy, extrasolar planets, space with tags astronomy, extrasolar planets, Science, SETI, space on 11/12/07 by Curtis

| | | | | | | |

Skymania News reports that astronomers working at California’s Lick Observatory have isolated the identity and certain characteristics of an Earth-like planet orbiting 55 Cancri, a star 41 light years distant from our own Sun and remarkably similar in physical characteristics such as core composition, spectrum, and temperature.

The discovery of this planet, approximately 45 times the mass of Earth and located within its star’s “habitable zone”—the orbital stratum in which conditions for the formation of Earth-like life would be optimal—demonstrates concretely what astronomers and philosophers have speculated for centuries: that our own star system, while quite special to us, is far from categorically unique.

While it would certainly be “jumping the gun” to assume that such a planet harbors life simply because of the existence of an optimal configuration, the most profound implication of the discovery—in harmony with other discoveries about extrasolar worlds which continue to surface as technology and techniques improve—is that, in its ability to support life, our own world is hardly the beneficiary of a singular providence of chance or “design.”

It is the fifth planet to be identified in orbit around the star 55 Cancri, a star very similar in type and age to our own Sun, making it a virtual twin of our own solar system.

The star, which is dimly visible to the naked eye in the constellation of Cancer, now holds the record for the number of worlds in orbit, after our own Sun. It lies just 41 light-years away - right on our cosmic doorstep.
Scientists said the new planet is 45 times the mass, or size of the Earth, and has a year 260 days long - the time it takes to orbit 55 Cancri. It was found by measuring the tiny wobble it causes to the star as it orbits. Detecting this was a triumph for the astronomers and took them 18 years of study from Lick Observatory, California, because it had to be separated from the effects of the other planets.

The planet is 72.5 million miles from 55 Cancri, a little less than the distance of the Earth from the Sun, but at an ideal distance for the warmth that life as we know it would need to exist.

Geoff Marcy, of the University of California, said last night: “The discovery has me jumping out of my socks. We now know that our own Sun and its family of planets is not unusual.”

He said that if there is a moon going around this new planet, it would have a rocky surface. Water could form lakes or seas and produce the conditions for life to begin. But he added: “Then all bets are off as to how life could evolve on that moon.”

Fellow discoverer Debra Fischer, of San Francisco State University, said she expected that other Earth-like planets could exist in the star’s habitable zone.

She said: “I bet that gap is not empty.”

She added: “55 Cancri is very much like our own sun. It is about the same size and the same age. It is a solar system that is packed with planets. It has profound implications for how we search for Earth-like planets.”

She went on: “The gas-giant planets in our solar system all have large moons. If there is a moon orbiting this new, massive planet, it might have pools of liquid water on a rocky surface.”

Leave A Comment »

Austin, TX to Require Zero-Energy Homes by 2015

Posted in Environment, Global Warming, Science, Texas, U.S. News, climate change, ecology, economy, energy with tags climate change, ecology, economy, energy, Environment, Global Warming, Science, Texas, U.S. News on 10/21/07 by Curtis

| | | | | | | |

Jetson Green writes on an Austin, Texas city initiative that will ramp up energy efficiency standards through 2015. The big surprise? It may actually save money in the long run:

The City of Austin, after a year of serious research by the Zero Energy Capable Homes Task Force, announced a huge initiative towards requiring all new single-family homes to be zero-energy capably by 2015. Here’s how it works. Today, the city adopted the first in a series of code amendments and a road map of code amendments that will be implemented through 2015. Due to this first series of changes, roughly 6500 new homes built in Austin will be about 20% more efficient. Through 2015, as the code changes ratchet up the efficiency baseline, homes will end up using about 65% less energy than those built today. Then, owners will have the option of adding solar or some other clean tech to get the home to zero energy status.

Speaking of the Zero Energy Homes Initiative, Mayor Will Wynn said, “We’re taking action today that will lower the cost of utility bills, make housing more affordable, help improve air quality and take critical steps in the fight against global warming.“

I’m always a bit startled by the phrase “fight against global warming.” I suppose it is more politically neutral than the “fight against industrial excess.”

2 Comments »

British University: Oceans Soaking Up Less CO2

Posted in Environment, Global Warming, Science, UK news, climate change, ecology, oceans with tags climate change, ecology, Environment, Global Warming, Science, UK news, World News on 10/21/07 by Curtis

| | | | | | | |

From the BBC News:

The amount of carbon dioxide being absorbed by the world’s oceans has reduced, scientists have said.

University of East Anglia researchers gauged CO2 absorption through more than 90,000 measurements from merchant ships equipped with automatic instruments.

Results of their 10-year study in the North Atlantic show CO2 uptake halved between the mid-90s and 2000 to 2005.

Scientists believe global warming might get worse if the oceans soak up less of the greenhouse gas.

Researchers said the findings, published in a paper for the Journal of Geophysical Research, were surprising and worrying because there were grounds for believing that, in time, the ocean might become saturated with our emissions.

The world’s oceans, like the terrestrial biomes taken as a whole, provide an important carbon ’sink’ through which atmospheric carbon dioxide levels are regulated. Algal blooms that feed on carbon dioxide are one of the main mechanisms through which the ocean participates in the carbon cycle, but, as far as we know, there is only so much that they can handle before saturation begins to occur.

Mounting evidence has suggested to many scientists that the ocean’s regulation of CO2 is a finely-tuned process capable of maintaining an equilibrium in all but the most extreme circumstances. The very real concern of these scientists is that, after over a century of virtually unfettered human industrial emissions, such an extreme circumstance may be here or presently on its way.

Leave A Comment »

Gore, UN-IPCC Win Nobel Peace Prize

Posted in Al Gore, Education, Environment, News, Nobel Peace Prize, Nobel Prize, Science, UN, USA, United Nations, World News, climate change, economy, environmentalism with tags Al Gore, climate change, economy, Education, Environment, News, Nobel Peace Prize, Science, United Nations, World News on 10/12/07 by Curtis

| | | | | | | |

Former U.S. Vice President and 2000 Presidential Candidate Albert Gore, Jr. has been awarded the 2007 Nobel Peace Prize for his work to bring the attention of policymakers and the public to the problems posed by anthropogenic (manmade) climate change. He shares this prize with the United Nations Intergovernmental Panel on Climate Change (UN-IPCC), a consortium of hundreds of climate scientists and other natural scientists from around the world which works to review the literature on climate change and to make sound policy recommendations to the UN and to governments.

At a press conference following the Nobel awards ceremony, Mr. Gore told reporters that climate change is the “most dangerous challenge we’ve ever faced,” according to The Guardian.

“It truly is a planetary emergency,” said Gore. “We have to respond quickly. I’m going back to work right now. This is just the beginning.”

On his sentiments at being the recipient of such a prestigious honor, Mr. Gore reflected, “I am deeply honored to receive the Nobel Peace Prize. This award is even more meaningful because I have the honor of sharing it with the IPCC - the world’s pre-eminent scientific body devoted to improving our understanding of the climate crisis.”

Gore’s interest in environmental safeguards reaches back to his days as a U.S. senator, but it was not until after his defeat by George W. Bush in the Presidential elections of 2000 that he became widely known as a strong advocate for sweeping reforms in governmental and corporate policy to ameliorate the clear and irreversible environmental damages caused by human industry. His 2006 documentary An Inconvenient Truth has served as a centerpiece for this campaign. The film won an Academy Award for best documentary feature, and another for best original song (by Melissa Etheridge).

An Inconvenient Truth has been greeted favorably by a large majority of scientists and political progressives who are well-aware of the immense potential dangers of climate change, and has received scorn from hardliner conservatives and a majority of the governmental representatives of large-scale industry and commerce. It was recently the subject of debate in the British High Court after the UK Government announced that it would provide a copy of the DVD to every secondary school in England and Wales. A London magistrate of the Court ruled on October 10 that the film is “broadly accurate” and only occasionally deviant from consensus, and that its hypotheses are well-supported in the literature. The governments of Spain and Belgium, among others, have widely circulated the film. Gore’s Nobel citation praises him as the individual who has done the most to bring public awareness to climate change over the past several years.

U.S. President George W. Bush famously said “Doubt it” when once asked if he planned to see Gore’s film. Australia’s Prime Minister John Howard, a staunch Bush ally, quipped “I don’t take policy advice from film” when refusing to meet with Gore during an unofficial visit to Australia. Industrial protectionism and the profit-centric animus of global capitalism continue to pose major obstacles to meaningful environmental policymaking.

The UN-IPCC has continually ramped up its predictions and recommendations in accordance with a growing preponderance of scientific evidence for the seriousness of anthropogenic climate change. It periodically publishes analyses and recommendations to world governments, recommendations which frequently fall upon deaf ears.

4 Comments »

Rationalism and Empiricism

Posted in Science, empiricism, knowledge, philosophy, rationalism with tags empiricism, knowledge, philosophy, rationalism, Science on 10/7/07 by Curtis

| | | | | | | |

There is a driving force behind a mystery that we cannot understand, and it includes more than reason alone . . .who knows what form the forward momentum of life will take in the time ahead or what use it will make of our anxious searching? The most that any one of us can seem to do is to fashion something—an object or ourselves—and drop it into the confusion, make an offering of it, so to speak, to the life force.

-Ernest Becker
The Denial of Death, 1973
Pulitzer Prize for Non-fiction, 1974 (posth.)

“To them, I said, the truth would be literally nothing but the shadows of the images . . . and if he is compelled to look straight at the light, will he not have a pain in his eyes which will make him turn away to take refuge in the objects of vision which he can see? . . . When he approaches the light his eyes will be dazzled, and he will not be able to see anything at all of what are now called realities.”

-Plato

The Republic

PROJECT -ISM, No. 2.

Plato’s rationalism, in essence, is embodied by his Allegory of the Cave from which the quote above is taken. In The Republic, Socrates asks his audience to imagine several men held captive deep inside a cave, chained tightly to a wall so that they can only face forward. Atop this wall behind them, he said, we should imagine a blazing fire; and when the captors of these men pass before the fire, their shadows are projected onto the wall in front of the unlucky inmates. Socrates points out that, eventually, the prisoners would come to regard the shadows as the true forms of that which exists—as things unto themselves and not as shadows. Then he asks us to imagine that one of the prisoners escapes into the sunlight and beholds, for the first time, the dazzlingly illuminated forms of the greater and more majestic cosmic reality. This splendid but laborious emergence was Plato’s way of constructing a metaphor for the progression from a commonsense, practical, but static and incomplete worldview based on experience (represented by the shadows) into a more dynamic, circumspect, and realistic view of the Universe obtainable only through reason (which is represented, of course, by the sunlight).

Ernest Becker’s The Denial of Death is really not as austere as the title might suggest; in fact, I would venture the statement that it is, to modern sensibilities, an indispensable volume for any student of psychology, sociology, anthropology, or philosophy. In this book, Becker lovingly dismantles Freud’s psychosexual motivational theories—which he regards as the noteworthy work of a great scientist, but discolored by Freud’s own neuroses and tendencies to perversion—and, enlisting the help of men such as Otto Rank and Norman O. Brown, replaces them with a picture of man as a uniquely rational animal constantly confronted with the knowledge of his own mortality. This “terror of death,” for Becker, is a much more tenable and constructive explanation for human motivation. One implication of Becker’s theory is that an overzealous devotion to rationalism (or, we might say conversely, an overzealous refutation of empiricism) is a tendency to be expected of mortal creatures wishing to escape the preponderance of empirical evidence for their irreversible and permanent mortality.

Encyclopédie Frontispiece The student of philosophy is typically presented with rationalism and empiricism as conflicting epistemological mores which have been unable to peaceably coexist throughout history. In reality, the two concepts are not mutually exclusive, and there has never been a philosopher who has wholeheartedly committed himself or herself to one or the other without exception of any kind. We retrospectively describe David Hume as an “empiricist” and René Descartes as a “rationalist,” and with good reason, but it must be recognized that these terms are more relativistic than categorical.

In this, the second part of Project -ism, I want to discuss the differences between rationalism and empiricism—the strengths and weaknesses of both—and also to divulge their inseparability and their complementary natures.

Epistemology can be defined as the study of knowledge—of what does and does not constitute it, and of its limits and usages. The implicit equivalence of knowledge and truth is an important part of the rationalist/empiricist conflict, as we shall quickly see; it also provides the key through which the issue is disentangled.

Rationalism as an epistemological approach dates back to the pre-Socratics and to Plato, who believed in the self-sufficiency of reason. For these philosophers, sensory information was often deceptive. Consider the apparent size of the moon: there is nothing about the appearance of the moon in the sky which would suggest, in and of itself, that the moon is any larger than a 25-cent piece. For the classical rationalist, one arrives only at the truth through the operation of reason upon sensory data.

Empiricism, in contrast, is the view that truths are arrived at only through the validation of rational belief through sensory experience. For the empiricist, there is no such thing as the ‘innate idea’ or a priori knowledge. All knowledge is derived from sensory data—otherwise, there is nothing to rationalize in the first place. No matter how self-evident a proposition might seem, the empiricist requires a concrete test against observations of the natural world in order to grant such a proposition the property of truth. British empiricism was founded in large measure upon the ideas of John Locke (pictured), who spoke of the mind as a tabula rasa—a ‘clean slate’ upon which experiences leave their marks. The word ‘empiricism’ is derived from the Greek εμπειρισμός (empeirismós), meaning, roughly, “experience.”At this point, it would be wise to say something of the concepts of a priori and a posteriori knowledge:

A priori knowledge is most commonly defined as knowledge that is the product of reason alone. As such, all statements which are a priori true are tautologies (self-evident propositions).
A posteriori knowledge is most commonly defined as knowledge that can only be gained through sensory experience.

As an example, Jerry Fodor once proposed the following: the statement “King George V reigned from 1910 to 1936″ is an example of a posteriori knowledge, because one can only gain this knowledge through experience—it is something of the external world which is learned; but the statement “If George V reigned at all, then he reigned for a while” is an example of a priori knowledge, because it is something that can be deduced rationally absent any supporting data.

A priori knowledge can be viewed as the product of deductive reasoning, while a posteriori knowledge is the fruit of inductive reasoning.

With the early modern philosophers, and specifically with Descartes, came a renaissance of the Pythagorean idea that mathematics represents a kind of a priori knowledge or pure reason. The British empiricist David Hume referred to a priori knowledge as ‘Relations of Ideas’ and to a posteriori knowledge as ‘Matters of Fact.’ Consider the following, from Section IV of his An Enquiry Concerning Human Understanding:

20. All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain. . . Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the Universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.

21. Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise tomorrow is no less intelligible a proposition . . . than the affirmation, that it will rise. . . It may, therefore, be a subject worthy of curiosity, to enquire what is the nature of that evidence which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory.

Circle - Pi According to Hume, we can imagine, however extraordinarily unlikely we might suppose it to be, waking at 7 a.m. to find that it is still night-time, that our face of the Earth has not yet turned into the sunlight and that the stars are still twinkling in the midst of the great blackness; we cannot imagine a circle whose circumference is not equal to its diameter times the value π.

This is because the relationship between the radius or diameter and the circumference of the circle is part of the definition of a circle, and because the definition of a definition is a description which holds in all cases. Thus, we might encounter a thing in nature which would appear to the senses to be circular; but we could not say without precise measurements and calculations whether or not it actually were circular. The Earth, for example, is not spherical. It is roughly spherical. So, if we are to prove the truth of the statement “This is a circle” with reference to a particular object of scrutiny, we cannot do so without dividing its circumference by its diameter and obtaining an approximation of π, or some equivalent operation. Now, we could communicate with one another about an ostensibly circular object in a way that would be effective for most practical purposes, without ever finding the need to resort to such precision. But if we are to prove that the object is circular, we must show that it conforms to the preconceived definition. Thus, in a majority of like cases, we could well be speaking of something not necessarily circular as if it were, without any appreciable effect upon our experience, because the thing seems circular enough. Thus, for Hume, empirical observation and methodical comparison was the only path to absolute knowledge.

The great Immanuel Kant (pictured) credited Hume’s text with “awakening him from his slumber” and causing him to question the tenets of rationalist philosophy. In his Critique of Pure Reason, Kant attempted to bridge rationalism and empiricism, while refuting Hume’s premise that only the empirically testable is absolutely true. He largely agreed with Locke’s characterization of the mind as tabula rasa, admitting that there can be no knowledge without experience; but he disagreed that all knowledge must arise from experience, noting that, by the comparison of experiences, we gain valid information which is not the result of any particular experience. Kant attempted to define this as synthetic a priori knowledge, and argued that the axioms of geometry are examples of this kind of knowledge in that they logically follow from fundamental truths without having to be proven in relationship to some aspect of the external world, but that they can be empirically proven even though they did not arise from empirical observation. Wasting no time, Kant poses his ideas in considerable detail right at the outset of the right formidable Critique:

There can be no doubt that all our knowledge begins with experience. For how should our faculty of knowledge be awakened into action did not objects affecting our senses partly of themselves produce representations, partly arouse the activity of our understanding to compare these representations, and, by combining or separating them, work up the raw material of the sensible impressions into that knowledge of objects which is entitled experience? In the order of time, therefore, we have no knowledge antecedent to experience, and with experience all our knowledge begins. But though all our knowledge begins with experience, it does not follow that it all arises out of experience. . .

For it may well be that even our empirical knowledge is made up of what we receive through impressions and of what our own faculty of knowledge (sensible impressions serving merely as the occasion) supplies from itself. If our faculty of knowledge makes any such addition, it may be that we are not in a position to distinguish it from the raw material, until with long practice of attention we have become skilled in separating it. This, then, is a question which at least calls for closer examination, and does not allow any off-hand answer . . .

Kant arrived eventually at the idea which Schopenhauer wrote “produces a fundamental change in every mind that has grasped it” and which I formulated independently—and far less eloquently—in Dualism and Monism, Project -ism No. 1: that we cannot understand the world as something which exists in and of itself (Kant: das Ding-an-Sich) apart from our cognition of it.

We can see, then, that in the most general possible sense of the word ‘knowledge,’ both empirical induction and rational deduction are capable of producing knowledge. But does either type of knowledge represent the truth moreso than the other? If not, what is the purpose of any debate between rationalism and empiricism? Wittgenstein had something further to say of this in his Tractatus from the early 20th Century:

6.37 A necessity for one thing to happen because another has happened does not exist. There is only logical necessity.

6.371 At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena.

6.372 So people stop short at natural laws as something unassailable, as did the ancients at God and Fate. And they are both right and wrong; but the ancients were clearer, in so far as they recognized one clear terminus, whereas the modern system makes it appear as though everything were explained.

Wittgenstein does not postulate that science and empiricism are useless. Indeed, modern medicine and numerous other technologies would seem to adequately demonstrate that, in terms of usefulness, science is far superior to supernatural mysticism. Wittgenstein’s argument is against knowledge as truth, and this argument is in line with his insistence that the greatest philosophical quandaries are, in essence, linguistic quandaries.

Microchip Let us return to what Kant wrote: “For it may well be that even our empirical knowledge is made up of what we receive through impressions and of what our own faculty of knowledge supplies from itself.”

This is the skeleton of the model of the mind as a computer with I/O capabilities! Observe:

What we receive through impressions - Data which is retrieved from the sensory organs, which function as input devices.
What our own faculty of knowledge supplies from itself - Analytical data which is the output of the mind, which functions as a processor capable of modifying its own software.

Framed within this scaffolding, we begin to conceive of three things which are critical to understanding the complementary natures of empiricism and rationalism:

All knowledge is rational by definition. Knowledge is analytical data which is the product of the processing of raw data or of other analytical data—this processing is what Kant describes as “what our own faculty of knowledge supplies from itself,” which is the process of rationalization.
Empirical methods are required to determine the self-consistency of knowledge, and this property of consistency grants knowledge a character that cannot be imparted through rational activity alone. For instance, philosophers traditionally characterize the formula C=πd as an a priori piece of knowledge defining the key formative properties of a circle. But only by drawing numerous circles, taking the appropriate measurements, and performing the necessary calculations can we show the consistency of this piece of knowledge.
Self-consistency of knowledge does not equate to the consistency of knowledge with reality—ergo, there is no “absolute truth.” In order to show that our formula for the circumference of a circle were true in all cases, we would have to draw infinitely many circles. This is not something we are capable of doing, so we choose an arbitrary stopping point. But to state that 10,000 affirmations of the formula is equivalent to the affirmation of the formula in all cases is clearly fallacious. Thus the limitations of rational knowledge and empirical knowledge are intertwined inseparably. There is no truth, only degrees of demonstrable consistency for a given purpose—and that this purpose is in every case given is essential to any meaning that the knowledge might have.

We have said that all a priori knowledge not derived from experience must take the form of tautology, the self-evident proposition. For instance, from the formula C=πd, we can derive a priori the formula 1/2(C)=1/2(πd), but this formulation contains no new information. Likewise, we could show, most unempirically, that π=C/d; but this, also, is merely reiteration, or the manipulation of forms.Therefore, to my mind—and the point at which I depart from Kant and some others—those propositions which are a priori are, in fact, not knowledge. This is the danger of equating the a priori with rationalism and the a posteriori with empiricism, a false equation if ever there was one. Knowledge consists of rationalization, but knowledge based on extant analytical data does not constitute a priori knowledge any more than knowledge based on fresh empirical data. This appears to be a function of neuroarchitecture, of the way in which sensory data is mapped in the mind. We can rewrite our mental software, but we cannot rewrite the firmware or reconstruct the hardware.

Rationalism and empiricism are not competing methods, but necessarily complementary ones. The friction between them arises principally from Quixotic quests to demonstrate the supremacy of one over the other, when the more realistic perspective follows from the acknowledgement of the necessity and inherent inadequacies of each. The conception that either is more adequate than the other as a digging tool for truth has been, I hope, demonstrated to be nonsensical, since the concept of truth as constant and infinite is illusory.

To return to the Platonic Allegory of the Cave, we can see that the escaped prisoner cowering in the sunlight is better off than his enchained peers, but still bound by gravity and the confines of his own skull after all.

6 Comments »

	Curtis on About the Blog
	Curtis on Maury Povich, have I got one f…
	Curtis on Shoring up the economy and put…
	Curtis on The Joose is no longer lo…
	Curtis on Un peu de l’impressionni…
	opit on Un peu de l’impressionni…
	opit on The Joose is no longer lo…
	opit on Maury Povich, have I got one f…

can’t see the forest

Archive for Science

Not such a bright guy? Neither are his little guys.

Implant Works to ‘Read Man’s Thoughts’

Exponents, Logarithms, and the Number e

Schizophrenia: An Unpleasant Side Effect of Natural Selection?

The Chutzpah of Intelligent Design

55 Cancri - A Home Away from Home?

Austin, TX to Require Zero-Energy Homes by 2015

British University: Oceans Soaking Up Less CO2

Gore, UN-IPCC Win Nobel Peace Prize

Rationalism and Empiricism

RSS Feed

Pages

Tags in the Forest

Latest Comments

Blogroll

Top Posts

What's Done Been Told