Irrational Numbers Metaphor

This is kind of a whimsical post, perhaps you may find it of very questionable relevance to a psychiatry blog.

I invite some input from any number theory experts out there, perhaps some of my thinking about the following subject is erroneous.

Irrational numbers are numbers which cannot be expressed as a ratio of integers. So, for example, the square root of 2 is irrational (it is approximately, but not exactly 1.414; it can be visualized as the distance diagonally across a square which has each side of length=1). The number pi (the ratio of a circle's circumference to its diameter) is irrational, approximately 3.14. The natural exponential base e is irrational, approximately 2.7. If we attempt to express an irrational number in decimal form, we can only ever get an approximation. The digits will keep on going forever, in a non-repeating fashion.

A hypothesis I have about the digit expansion of an irrational number is that the sequence represents a form of true randomness. At one point I did plot out the frequencies of digits in an expansion of pi to a million digits or so, then performed some statistical tests on this, and determined that the results are consistent with random ordering. They MUST be "random", for if they weren't, the number could not be irrational. I would invite a number theorist to show me a proof of this. My idea about randomness invites a philosophical, or mathematical, discussion, about what the meaning of true randomness really is.

But the digits of irrational numbers are calculable. That is, the millionth, or trillionth, digit, in the decimal expansion of pi, can be determined, systematically, through various algorithms. The number e can be calculated in a number of ways (this is a way I discovered as a child, playing with my calculator: take (1+1/n) multiplied by itself n times, with the calculation becoming more and more accurate as n grows larger--only perfectly accurate, though, when n reaches infinity).

So, I am claiming that the digits are calculable, yet randomly ordered. This is a seeming contradiction.

However, I believe there is no simple formula for the "nth" digit of pi. In order to get the "nth" digit, at least n arithmetic steps must be taken. That is, computational work must be done in order to do the calculation, and more computational work is required in order to reach a more precise result, which is at least linearly proportional to the level of precision desired.

Since all computational work requires energy, and there is a finite amount of energy available in the universe, let us suppose that we use all the mass-energy of the universe to perform computational work to determine as many digits of pi, for example, as is possible. (this would involve, in our thought experiment, harnessing all of the great nuclear energies from the stars, etc. to power a computational device just for this task)

Now, having generated all of these digits (I suspect there would be over 10^1000 digits generated, using all the energy of the universe efficiently for this task), we still only have an approximation to the number pi. The NEXT digits of pi are theoretically calculable, but cannot be calculated or known, because we have used all available computational energy.

Thus, we have calculable digits, which yet cannot be known, because there is not enough energy in the universe to do the calculations to know them.

There is something almost mystical about this: any sequence of digits, for example, randomly conceived in the mind, must correspond to a sequence of digits in the unknowable expansion of pi (in that realm over 10^1000 digits into the expansion), based on the laws of probability.

Something that we can prove is outside the realm of human knowledge is actually part of the ordinary daily products of our imagination.

As an added concept related to this, imagine what your entire life history would look like, translated into a sequence of digits -- perhaps this would include a few thousand pages of text, a few million images, together with the entire sequence of your genome, all transformed into a digit sequence, maybe a few trillion digits long.

It can be shown that this sequence -- an intimate representation of your identity -- must occur at some point in the decimal expansion of all irrational numbers, including pi. (suppose the sequence representing your life story is 10 trillion digits long; then the probability of your sequence occurring starting at or before the nth position in pi's expansion is 1-(1-1/(10 trillion))^n, assuming that pi's digit expansion behaves as a random sequence. With this assumption, once you are into pi's expansion by 10 trillion digits, there's a 63% chance that your sequence will have shown up (interestingly, this probability is approximately 1-1/e). And the more digits you go into pi's expansion, the more likely it is that "your" sequence will show up; this probability converges towards 100% as the number of digits approaches infinity. Actually, we could go on to say that "your" sequence actually recurs, an infinite number of times, in pi's expansion!

In our imagination, we can conceive an ideal circle, and we can imagine the ratio between its circumference and its diameter. That is pi exactly. We have imaginatively visualized something, with perfect precision, something that cannot be expressed logically with perfect precision.

There is a life lesson in this, I think. Be open to possibility. That which is seemingly impossible may require an imaginative re-framing to see that it was always in front of you, available to you, part of "ordinary" daily life. And there can be more to simple relationships than meets the eye -- dividing a circumference by a diameter yields a number which contains information paralleling all known information in the universe, including the story of yourself.

Moclobemide is a Good Antidepressant

The antidepressant moclobemide is a reversible monoamine oxidase inhibitor. Once again, this is a drug that was frequently prescribed for a time, but has subsequently faded in popularity.

It was released in the late 80's; around 1990 many studies came out, comparing moclobemide with other antidepressants, including tricyclics and fluoxetine, showing that it worked just as well for treating depression. Many of these studies were published in Scandinavia. There have been very few clinical studies since then. Part of the reason may be that moclobemide was never approved in the U.S. (I do not understand why not).

Moclobemide has also been used effectively to treat social phobia.

In my opinion, it is a neglected option in treating depression. Because it has faded in popularity, it is usually tried as a third-line medication. For this reason, it is prescribed to patients who are more likely to have a more refractory depression. For this reason, it is less likely to be seen to help as much; this leads to clinicians pronouncing it ineffective, and not prescribing it. If it was prescribed as a first-line agent, I think we would see that it works pretty much as well as any other antidepressant.

Its advantages relate to the side-effect profile: its side effects in general are probably closest to placebo among all the antidepressants. And there are minimal or no sexual side effects with moclobemide, compared to the SSRI's. Here's a reference:

http://www.ncbi.nlm.nih.gov/pubmed/10974600

Other references:

http://www.ncbi.nlm.nih.gov/pubmed/17168253
{a 2006 meta-analysis showing that moclobemide works as well as SSRI's}

http://www.ncbi.nlm.nih.gov/pubmed/16702988
{a 2006 article from the British Journal of Pharmacology suggesting that moclobemide may have neuroprotective or even neurogenerative effects in the hippocampus}

http://www.ncbi.nlm.nih.gov/pubmed/12595913
{a 2003 review}

Addendum:

There was one case series study published in 2000 by Magder, Aleksic, and SH Kennedy, describing the successful use of very high-dose moclobemide in combination with lithium and/or trazodone for treatment-resistant depressed patients. The doses used were up to 1500-1650 mg/day, which is much higher than the usual maximum of 600 mg. They advocated using an MAOI diet at these doses. Moclobemide was well-tolerated, and the patients appeared to benefit over 1-2 years of follow-up. It's worth looking at this brief article in its entirety, here's a link to the abstract:
http://www.ncbi.nlm.nih.gov/pubmed/10831036

Volunteering Improves Mental Health

Altruistic volunteering is beneficial for mental health.
There are several mechanisms by which this could happen:

1) the experience of giving one's time and energy for another in need is an intrinsic life joy
2) there are opportunities to build new friendships, with others who also are "practicing altruists"
3) the experience may allow you to discover new aspects of yourself, in terms of skills, pleasures, ambitions, etc.
4) the structure of the volunteer experience may be a "benevolent structure" motivating action in your day, challenging depressive symptoms which might keep you inactive or alone

Here is some evidence from the literature:

http://www.ncbi.nlm.nih.gov/pubmed/18381833
{this 2008 study from a gerontology journal, shows that people in their 60's who volunteer moderately have higher levels of well-being, after controlling for variables such as educational level, physical health, etc. People who didn't volunteer, or people who volunteered "too much", had lower levels of well-being}

http://www.ncbi.nlm.nih.gov/pubmed/18321629
{a 2008 study from the London School of Economics, showing that there is a direct causal relationship between volunteering and happiness; weekly volunteering increases the likelihood of being "very happy" by 16%, independent of income level--the data also suggest that the effect is more pronounced for people who volunteer more frequently}

http://www.ncbi.nlm.nih.gov/pubmed/11467248
{a 2001 study looking at data from 2681 people, showing that volunteering is associated with increased well-being in numerous domains, including happiness, life satisfaction, self-esteem, sense of control over life, physical health, and depression}

http://www.ncbi.nlm.nih.gov/pubmed/9718488
{a 1998 study showing that volunteering bolsters well-being in elderly persons who volunteer; also the people who are helped by the volunteers had reduced amounts of depression}


I think there should be some more prospective, randomized studies of volunteering and other altruistic activity in the treatment of mental illnesses.

If you are interested in volunteering in Vancouver, here is a place to start looking:


http://www.govolunteer.ca/cgi-bin/page.cgi?_id=16

Caffeine & Coffee : Health Benefits

So, is coffee good for you? Or is it bad for you?
How about decaf?

It seems that there are mixed messages out there, about health effects from things such as coffee or caffeine.

What does the evidence tell us?

The evidence base is extremely compelling --

Here is a link to a study by Lopez-Garcia et al. from Annals of Internal Medicine in 2008, involving over 100 000 people, over 18 years of follow-up. Such massive studies with long follow-up time are incredibly informative:

http://www.ncbi.nlm.nih.gov/pubmed/18559841

In the study, it shows clearly that coffee drinkers have lower overall mortality rates, mainly due to a reduction in rates of cardiovascular disease. It showed a modest reduction in mortality rates associated with decaffeinated coffee as well. The authors conclude that the potential health benefits from coffee are due to components in the coffee other than caffeine.

The graph on the top is copied from the paper, and summarizes the results from the study. You can click on the graph to expand it. Actually, the data as presented on the graph suggests that people are healthier who have 2-3 cups of coffee per day, compared to those who have just 1.
Perhaps the less desirable effects from just a single cup per day are due to the more pronounced "jolt" of caffeine that would happen in a person who is not used to drinking as much coffee. Perhaps this effect would offset the health benefit, at low doses. At higher doses, the body may become more tolerant to caffeine's anxiogenic effects.


Unfortunately, this study did not look at mental health effects from drinking coffee, or from caffeine intake.

In another large epidemiological study of over 1400 people followed over 21 years, it was found that those who consumed coffee in mid-life had a substantially lower risk of developing dementia. This association was true after adjustment for demographic differences, lifestyle, and vascular disease.
http://www.ncbi.nlm.nih.gov/pubmed/19158424

This case-control study from Archives of Neurology in 2007 showed an inverse association between coffee intake and development of Parkinson disease (i.e. this relationship suggests that coffee could protect the brain from disease such as Parkinson's). However, smaller case-control studies such as this one are much weaker than the large prospective studies cited above:
http://www.ncbi.nlm.nih.gov/pubmed/17420321

The following 2008 article from Sleep Medicine Reviews presents a more cautionary account of caffeine's effects, particularly with respect to causing a dependence phenomenon, and to disrupting sleep quality. However, a lot of the data cited in this article is absurd, such as showing that a dose of caffeine immediately before sleep causes sleep disruption! Bedtime doses of coffee are not a realistic reflection of most people's caffeine intake!
http://www.ncbi.nlm.nih.gov/pubmed/17950009

Here's an interesting reference to an article showing that the tendency for caffeine to cause sleep disturbance is a heritable trait. That is, some people might be vulnerable to caffeine-induced insomnia, whereas others could sleep well regardless of their caffeine intake:
http://www.ncbi.nlm.nih.gov/pubmed/17969472

Here's a case report of a person with schizoaffective disorder improving upon discontinuing heavy caffeine intake:
http://www.ncbi.nlm.nih.gov/pubmed/18455857


In summary, it appears that coffee drinking is not harmful. In most cases, it may in fact be good for you. However, pregnant women should minimize their use of coffee. For some people, caffeine may cause or exacerbate anxiety or insomnia, especially at higher doses.

Buspirone

Buspirone is another of those medications that was introduced in the 80's, and was marketed for the treatment of anxiety. Most of the published studies on buspirone were done around 1990.

While many antidepressants simply increase the amount of serotonin or other neurotransmitters by blocking neurotransmitter re-uptake into neurons, buspirone works by directly stimulating one of the target receptors for serotonin, called the 5HT-1A receptor.

As with many new drugs, there was a wave of enthusiasm, which eventually faded. At this point buspirone is rarely prescribed.

In my opinion, it could be a useful and well-tolerated adjunct, to try in the following situations:

1) to treat generalized anxiety disorder
2) to augment antidepressants (i.e. to add to an antidepressant which isn't working well enough)
3) to treat antidepressant-induced jaw or tooth grinding (bruxism)
4) to treat aggressive or self-injurious behaviour; it may be particularly helpful in elderly patients with dementia, or in mentally handicapped patients
5) to treat migraine (a common comorbid problem among depressed or anxious patients)
6) to help with opiate withdrawal
7) to help quit smoking

Side effects are usually mild and subside with time; they include dizziness, nausea, sweating, or nervousness. About 10% of people in the clinical trials of buspirone discontinued the medication due to side effects.

Buspirone is metabolized through the cytochrome P450 3A4 system in the liver; because of this its levels in the body can be substantially increased by other medications or grapefruit juice, so these types of interactions have to be considered when choosing a dose.

I've been curious to revisit the evidence base for buspirone; here is my review of the literature:

1) Using buspirone as an augmentation to antidepressants, for treatment of depression:

http://www.ncbi.nlm.nih.gov/pubmed/17628435
{a good, important study from NEJM in 2006: 565 depressed patients who had not remitted despite receiving high-dose citalopram, were given augmentation therapy with either bupropion SR or buspirone. That is, the bupropion or buspirone was added onto their daily regimen of citalopram, and the patients were followed over at least 7 weeks. Both groups did similarly well, with about 30% of both groups having a remission. The bupropion group did slightly better in a few ways. Unfortunately there was no placebo augmentation group}

2) Treating generalized anxiety:

http://www.ncbi.nlm.nih.gov/pubmed/8666569
{a small study from 1996 showing that buspirone helps reduce anxiety symptoms in patients who also have mild depression; but the reduction in anxiety symptoms (about 50%) is only modestly different from placebo (about 35%) }

http://www.ncbi.nlm.nih.gov/pubmed/3320034
{this study from 1987 had a one-year follow-up of 700 patients. But it was open-label (no randomization, no placebo group). It did show that the patients taking buspirone for treatment of generalized anxiety showed sustained improvement, and tolerated the medication well}

http://www.ncbi.nlm.nih.gov/pubmed/17984162
{this 2007 study compares the effect sizes of numerous different medication treatments for generalized anxiety; buspirone fares particularly poorly, with a "non-significant" effect size of 0.17; SSRI's and venlafaxine do slightly better, and the novel anticonvulsant pregabalin actually does best. Complementary and alternative medications had a negative effect on symptoms, in this analysis. However, this meta-analysis is limited by the fact that most of the buspirone studies were done over 10 years ago and most of the results are from short-term treatment.}

http://www.ncbi.nlm.nih.gov/pubmed/2211567
{one of the small randomized studies comparing buspirone with a benzodiazepine for treatment of anxiety; the study shows similar effectiveness. Given that buspirone is non-addictive, it makes buspirone a more attractive option}


3) Treating other anxiety conditions:

http://www.ncbi.nlm.nih.gov/pubmed/2407755
{one of the studies showing that buspirone is NOT effective for treating panic disorder}

4) Improving cognitive function in schizophrenia:

http://www.ncbi.nlm.nih.gov/pubmed/17628435
{this 2007 study had a good randomized design, and 6 months of follow-up; it claimed in the abstract that buspirone had a beneficial effect on cognition when added to antipsychotics in schizophrenia -- but if you take a look at the actual data in the article, the differences in buspirone vs. placebo groups are very small. So I'm not impressed.}

5) Treating migraine:

http://www.ncbi.nlm.nih.gov/pubmed/16109114
{a small 2005 study in a headache journal looking at a group of 74 patients with migraine over 6 weeks of treatment; it showed that low-dose buspirone (10 mg) reduces migraine frequency by about 40%, and reduced anxiety scores by about 20%, both of which a substantial difference compared to placebo. The improvement in anxiety did not depend on the improvement in headache, they appeared to be separate, independent effects.}

6) Treating acute heroin withdrawal:

http://www.ncbi.nlm.nih.gov/pubmed/15876901
{an interesting 2005 study showing that 45 mg per day of buspirone can reduce symptoms of heroin withdrawal over a 2-week period; looking at the results directly, it appears that the effect is very substantial, that the buspirone almost eliminated withdrawal symptoms}

7) Helping quit smoking:

http://www.ncbi.nlm.nih.gov/pubmed/1739365
{a small 1992 study from Archives of Internal Medicine showing that buspirone helps with nicotine withdrawal, and may help people quit smoking}

8) Treating ataxia:

http://www.ncbi.nlm.nih.gov/pubmed/8806320
{another interesting study from Lancet in 1996, showing that buspirone helps improve symptoms of cerebellar ataxia, a type of brain disease which causes impaired balance & coordination}

9) Treating aggressive behaviours:

http://www.ncbi.nlm.nih.gov/pubmed/2016248
{a small study suggesting that buspirone can help reduce aggression and anxiety in mentally handicapped adults, without causing sedation or cognitive side-effects}

10) Treating bruxism:

http://www.ncbi.nlm.nih.gov/pubmed/10665633
{a 1999 study of 4 cases of SSRI-induced bruxism improving with buspirone}

11) Treating tardive dyskinesia:

http://www.ncbi.nlm.nih.gov/pubmed/8102622
{a 1993 study showing some improvement in tardive dyskinesia (a movement disorder) after treatment with buspirone for 12 weeks. However there are a few other case reports in the literature of buspirone causing worsened symptoms of various movement disorders, such as dystonias or myoclonus (twitching); but the incidence of such side effects appears to be very low}


12) Animal studies:

http://www.ncbi.nlm.nih.gov/pubmed/17312776
{in this study a badger in a zoo (!) was suffering agitation and engaging in self mutilation; "environmental enrichment" initially helped, but the behavioural problems still recurred. Buspirone ended up helping substantially, over an 18 month period, with no side-effects}

http://www.ncbi.nlm.nih.gov/pubmed/15766212
{in another animal study, buspirone helped reduce self-injurious behaviour in a group of rhesus macaques, and it seemed to help more than fluoxetine, with fewer side-effects}