“A Troublesome Inheritance” – I

One of the joys of a deep understanding of chemistry, is the appreciation of the ways in which life is constructed from the most transient of materials. Presumably the characteristics of living things that we can see (the phenotype) will someday be traceable back to the proteins, nucleic acids,and small metabolites (lipids, sugars, etc..) making us up.

For the time being we must content ourselves with understanding the code (our genes) and how it instructs the development of a trillion celled organism from a fertilized egg. This brings us to Wade’s book, which has been attacked as racist, by anthropologists, sociologists and other lower forms of animal life.

Their position is that races are a social, not a biological construct and that differences between societies are due to the way they are structured, not by differences in the relative frequency of the gene variants (alleles) in the populations making them up. Essentially they are saying that evolution and its mechanism descent with modification under natural selection, does not apply to humanity in the last 50,000 years when the first modern humans left Africa.

Wade disagrees. His book is very rich in biologic detail and one post about it discussing it all would try anyone’s attention span. So I’m going to go through it, page by page, commenting on the material within (the way I’ve done for some chemistry textbooks), breaking it up in digestible chunks.

As might be expected, there will be a lot of molecular biology involved. For some background see the posts in https://luysii.wordpress.com/category/molecular-biology-survival-guide/. Start with http://luysii.wordpress.com/2010/07/07/molecular-biology-survival-guide-for-chemists-i-dna-and-protein-coding-gene-structure/ and follow the links forward.

Wade won me over very quickly (on page 3), by his accurate and current citations to the current literature. He talks about how selection on a mitochondrial protein helped Tibetans to live at high altitude (while the same mutation those living at low altitudes leads to blindness). Some 25% Tibetans have the mutation while it is rare among those living at low altitudes.
Here’s my post of 10 June 2012 ago on the matter. That’s all for now

Have Tibetans illuminated a path to the dark matter (of the genome)?

I speak not of the Dalai Lama’s path to enlightenment (despite the title). Tall people tend to have tall kids. Eye color and hair color is also hereditary to some extent. Pitched battles have been fought over just how much of intelligence (assuming one can measure it) is heritable. Now that genome sequencing is approaching a price of $1,000/genome, people have started to look at variants in the genome to help them find the genetic contribution to various diseases, in the hopes of understanding andtreating them better.

Frankly, it’s been pretty much of a bust. Height is something which is 80% heritable, yet the 20 leading candidate variants picked up by genome wide association studies (GWAS) account for 3% of the variance [ Nature vol. 461 pp. 458 - 459 '09 ]. This has happened again and again particularly with diseases. A candidate gene (or region of the genome), say for schizophrenia, or autism, is described in one study, only to be shot down by the next. This is likely due to the fact that many different genetic defects can be associated with schizophrenia — there are a lot of ways the brain cannot work well. For details — see http://luysii.wordpress.com/2010/04/25/tolstoy-was-right-about-hereditary-diseases-imagine-that/. or see http://luysii.wordpress.com/2010/07/29/tolstoy-rides-again-autism-spectrum-disorder/.

Typically, even when an association of a disease with a genetic variant is found, the variant only increases the risk of the disorder by 2% or less. The bad thing is that when you lump them all of the variants you’ve discovered together (for something like height) and add up the risk, you never account for over 50% of the heredity. It isn’t for want of looking as by 2010 some 600 human GWAS studies had been published [ Neuron vol. 68 p. 182 '10 ]. Yet lots of the studies have shown various disease to have a degree of heritability (particularly schizophrenia). The fact that we’ve been unable to find the DNA variants causing the heritability was totally unexpected. Like the dark matter in galaxies, which we know is there by the way the stars spin around the galactic center, this missing heritability has been called the dark matter of the genome.

Which brings us to Proc. Natl. Acad. Sci. vol. 109 pp. 7391 – 7396 ’12. It concerns an awful disease causing blindness in kids called Leber’s hereditary optic neuropathy. The ’cause’ has been found. It is a change of 1 base from thymine to cytosine in the gene for a protein (NADH dehydrogenase subunit 1) causing a change at amino acid #30 from tyrosine to histidine. The mutation is found in mitochondrial DNA not nuclear DNA, making it easier to find (it occurs at position 3394 of the 16,569 nucleotide mitochondrial DNA).

Mitochondria in animal cells, and chloroplasts in plant cells, are remnants of bacteria which moved inside cells as we know them today (rest in peace Lynn Margulis).

Some 25% of Tibetans have the 3394 T–>C mutations, but they see just fine. It appears to be an adaptation to altitude, because the same mutation is found in nonTibetans on the Indian subcontinent living about 1500 meters (about as high as Denver). However, if you have the same genetic change living below this altitude you get Lebers.

This is a spectacular demonstration of the influence of environment on heredity. Granted that the altitude you live at is a fairly impressive environmental change, but it’s at least possible that more subtle changes (temperature, humidity, air conditions etc. etc.) might also influence disease susceptibility to the same genetic variant. This certainly is one possible explanation for the failure of GWAS to turn up much. The authors make no mention of this in their paper, so these ideas may actually be (drumroll please) original.

If such environmental influences on the phenotypic expression of genetic changes are common, it might be yet another explanation for why drug discovery is so hard. Consider CETP (Cholesterol Ester Transfer Protein) and the very expensive failure of drugs inhibiting it. Torcetrapib was associated with increased deaths in a trial of 15,000 people for 18 – 20 months. Perhaps those dying somehow lived in a different environment. Perhaps others were actually helped by the drug

More chemical insanity from neuroscience

The current issue of PNAS contains a paper (vol. 111 pp. 8961 – 8966, 17 June ’14) which uncritically quotes some work done back in the 80’s and flatly states that synaptic vesicles http://en.wikipedia.org/wiki/Synaptic_vesicle have a pH of 5.2 – 5.7. Such a value is meaningless. Here’s why.

A pH of 5 means that there are 10^-5 Moles of H+ per liter or 6 x 10^18 actual ions/liter.

Synaptic vesicles have an ‘average diameter’ of 40 nanoMeters (400 Angstroms to the chemist). Most of them are nearly spherical. So each has a volume of

4/3 * pi * (20 * 10^-9)^3 = 33,510 * 10^-27 = 3.4 * 10^-23 liters. 20 rather than 40 because volume involves the radius.

So each vesicle contains 6 * 10^18 * 3.4 * 10^-23 = 20 * 10^-5 = .0002 ions.

This is similar to the chemical blunders on concentration in the nano domain committed by a Nobelist. For details please see — http://luysii.wordpress.com/2013/10/09/is-concentration-meaningful-in-a-nanodomain-a-nobel-is-no-guarantee-against-chemical-idiocy/

Didn’t these guys ever take Freshman Chemistry?

Addendum 24 June ’14

Didn’t I ever take it ? John wrote the following this AM

Please check the units in your volume calculation. With r = 10^-9 m, then V is in m^3, and m^3 is not equal to L. There’s 1000 L in a m^3.
Happy Anniversary by the way.

To which I responded

Ouch ! You’re correct of course. However even with the correction, the results come out to .2 free protons (or H30+) per vesicle, a result that still makes no chemical sense. There are many more protons in the vesicle, but they are buffered by the proteins and the transmitters contained within.

A purely nonscientific post

On 14 June ’14 we celebrated our 50th wedding anniversary in London, England. Here is what we saw

Noon: Trooping the colors — the celebration of the Queen’s birthday. Huge crowds, many carrying backpacks. Huge police presence. We saw the queen riding in a carriage, princess Kate and husband, and at least 3 sets of mounted horsemen all wearing tall bearskin hats.
Nothing happened a la Boston marathon (fortunately). Talked to some of the police who told us that there were many secret service types embedded in the crowd.

1 PM: While eating lunch in a nearby Italian bistro, police came down the street, and taped off half. The were followed by 2,000 or so members of the Jesus Army, singing and dancing and inviting all to march with them down to nearby Trafalgar Square. All ages, nationalities were present (no burkas though of which there were many everywhere we went in downtown London).

2 PM: While walking to St. Paul’s a few miles away for Evensong at 6:00 — more police, more tape. Then cheers went up as about 200 nude bicyclists rode past. No one in the crowd said put it back on, but these weren’t playboy and playgirl centerfolds.

3 PM: Trafalgar square, with the Jesus Army — a stage set up and a Christian rock band blasting away. Happy crowd. Onlookers polite if bemused. Nude cyclists not in evidence.

4 – 5:30 PM — While leisurely walking to St. Paul’s, the nude bicyclists would unexpectedly appear from a side street and then disappear down another just as quickly. They certainly caught our attention, too much to see what the reaction of the ladies in burkas and head scarves was (I wish I’d looked).

6 PM: St. Paul’s Cathedral — it must be experienced, pictures simply don’t do it justice. We were able to sit in the apse in the seats for the choir, listening to the service and the music, perhaps 10 – 20 feet away from clergy and 40 feet from the choir. As a musician, it was fantastic to hear liturgical choral music in the physical space it was written for. When the singing stopped, the enveloping sound took a few seconds to die away. Chilling and thrilling. A Bach organ fugue finished the recessional.

7 PM: My wife and I describe ourselves as hunter gatherers in bookstores, and Waterstone’s in Pickadilly Circus (a bit of Atlantic City moved to London) didn’t disappoint. Said to be the largest bookstore in Europe — very great browsing material, with lots of comfortable places to read. Glad to see Nicholas Wade’s book prominently displayed (about which there will be several posts). They’ll mail anything you buy to the USA for a 10% surcharge, another bookstore was charging 9 pounds a book. Our stuff arrived in under 10 days quite well packed and intact.

9 PM: Dinner at Cichetti’s near Pickadilly Square — an interesting Italian restaurant with excellent food, with an unusual style of serving and ordering.

Next up:

Possibly a few sociological and historical notes about our 2 weeks in England.

A lengthy review and page by page commentary on Nicholas Wade’s book (thanks for the gift Ashutosh).

The perfect aphrodisiac ?

We’re off to London for a few weeks to celebrate our 50th Wedding Anniversary. As a parting gift to all you lovelorn organic chemists out there, here’s a drug target for a new aphrodisiac.

Yes, it’s yet another G Protein Coupled Receptor (GPCR) of which we have 800+ in our genome, and which some 30% of drugs usable in man target (but not this one).

You can read all about it in a leisurely review of “Affective Touch” in Neuron vol. 82 pp. 737 – 755 ’14, and Nature vol. 493 pp. 669 – 673 ’13. The receptor (if the physiological ligand is known the papers are silent about it) is found on a type of nerve going to hairy skin. It’s called MRGPRB4.

The following has been done in people. Needles were put in a cutaneous nerve, and skin was lightly stroked at rates between 1 and 10 centimeters/second. Some of the nerves respond at very high frequency 50 – 100 impulses/second (50 – 100 Hertz) to this stimulus. Individuals were asked to rate the pleasantness of the sensation produced. The most pleasant sensations produced the highest frequency responses of these nerves.

MRGPRB4 is found on nerves which respond like this (and almost nowhere else as far as is known), so a ligand for it should produce feelings of pleasure. The whole subject of proteins which produce effects when the cell carrying them is mechanically stimulated is fascinating. Much of the work has been done with the hair cells of the ear, which discharge when the hairs are displaced by sound waves. Proteins embedded in the hairs trigger an action potential when disturbed.

Perhaps there is no chemical stimulus for MRGPRB4, just as there isn’t for the hair cells, but even so it’s worth looking for some chemical which does turn on MRGPRB4. Perhaps a natural product already does this, and is in one of the many oils and lotions people apply to themselves. Think of the chemoattractants for bees and other insects.

If you’re the lucky soul who finds such a drug, fame and fortune (and perhaps more) is sure to be yours.

Happy hunting

Back in a few weeks

A huge amount of work will need to be redone

The previous post is reprinted below the —- if you haven’t read it, you should do so now before proceeding.

Briefly, no one had ever bothered to check if subjects were asleep while studying the default mode of brain activity. The paper discussed in the previous post appeared in the 7 May ’14 issue of Neuron.

In the 13 May ’14 issue of PNAS [ Proc. Natl. Acad. Sci. vol. 111 pp. E2066 - E2075 '14 ] a paper appeared on genetic links to default mode abnormalities in schizophrenia and bipolar disorder.

From the abstract “Study subjects (n = 1,305) underwent a resting-state functional MRI scan and were analyzed by a two-stage approach. The initial analysis used independent component analysis (ICA) in 324 healthy controls, 296 Schizophrenic probands, 300 psychotic bipolar disorder probands, 179 unaffected first-degree relatives of schizophrenic pro bans, and 206 unaffected first-degree relatives of psychotic bipolar disorder probands to identify default mode networks and to test their biomarker and/or endophenotype status. A subset of controls and probands (n = 549) then was subjected to a parallel ICA (para-ICA) to identify imaging–genetic relationships. ICA identified three default mode networks.” The paper represents a tremendous amount of work (and expense).

No psychiatric disorder known to man has normal sleep. The abnormalities found in the PNAS study may not be of the default mode network, but in the way these people are sleeping. So this huge amount of work needs to be repeated. An tghis is just one paper. As mentioned a Google search on Default Networks garnered 32,000,000 hits.

Very sad.

____

How badly are thy researchers, O default mode network

If you Google “default mode network” you get 32 million hits in under a second. This is what the brain is doing when we’re sitting quietly not carrying out some task. If you don’t know how we measure it using functional mMRI skip to the **** and then come back. I’m not a fan of functional MRI (fMRI), the pictures it produces are beautiful and seductive, and unfortunately not terribly repeatable.

If [ Neuron vol. 82 pp. 695 - 705 '14 ] is true than all the work on the default network should be repeated.

Why?

Because they found that less than half of 71 subjects studied were stably awake after 5 minutes in the scanner. E.g. they were actually asleep part of the time.

How can they say this?

They used Polysomnography — which simultaneously measures tons of things — eye movements, oxygen saturation, EEG, muscle tone, respiration pulse; the gold standard for sleep studies on the patients while in the MRI scanner.

You don’t have to be a neuroscientist to know that cognition is rather different in wake and sleep.

Pathetic.

****

There are now noninvasive methods to study brain activity in man. The most prominent one is called BOLD, and is based on the fact that blood flow increases way past what is needed with increased brain activity. This was actually noted by Wilder Penfield operating on the brain for epilepsy in the 30s. When the patient had a seizure on the operating table (they could keep things under control by partially paralyzing the patient with curare) the veins in the area producing the seizure turned red. Recall that oxygenated blood is red while the deoxygenated blood in veins is darker and somewhat blue. This implied that more blood was getting to the convulsing area than it could use.

BOLD depends on slight differences in the way oxygenated hemoglobin and deoxygenated hemoglobin interact with the magnetic field used in magnetic resonance imaging (MRI). The technique has had a rather checkered history, because very small differences must be measured, and there is lots of manipulation of the raw data (never seen in papers) to be done. 10 years ago functional magnetic imaging (fMRI) was called pseudocolor phrenology.

Some sort of task or sensory stimulus is given and the parts of the brain showing increased hemoglobin + oxygen are mapped out. As a neurologist, I was naturally interested in this work. Very quickly, I smelled a rat. The authors of all the papers always seemed to confirm their initial hunch about which areas of the brain were involved in whatever they were studying. Science just isn’t like that. Look at any issue of Nature or Science and see how many results were unexpected. Results were largely unreproducible. It got so bad that an article in Science 2 August ’02 p. 749 stated that neuroimaging (e.g. functional MRI) has a reputation for producing “pretty pictures” but not replicable data. It has been characterized as pseudocolor phrenology (or words to that effect).

What was going on? The data was never actually shown, just the authors’ manipulation of it. Acquiring the data is quite tricky — the slightest head movement alters the MRI pattern. Also the difference in NMR signal between hemoglobin without oxygen and hemoglobin with oxygen is small (only 1 – 2%). Since the technique involves subtracting two data sets for the same brain region, this doubles the error.

How badly are thy researchers, O default mode network

If you Google “default mode network” you get 32 million hits in under a second. This is what the brain is doing when we’re sitting quietly not carrying out some task. If you don’t know how we measure it using functional mMRI skip to the **** and then come back. I’m not a fan of functional MRI (fMRI), the pictures it produces are beautiful and seductive, and unfortunately not terribly repeatable.

If [ Neuron vol. 82 pp. 695 - 705 '14 ] is true than all the work on the default network should be repeated.

Why?

Because they found that less than half of 71 subjects studied were stably awake after 5 minutes in the scanner. E.g. they were actually asleep part of the time.

How can they say this?

They used Polysomnography — which simultaneously measures tons of things — eye movements, oxygen saturation, EEG, muscle tone, respiration pulse; the gold standard for sleep studies on the patients while in the MRI scanner.

You don’t have to be a neuroscientist to know that cognition is rather different in wake and sleep.

Pathetic.

****

There are now noninvasive methods to study brain activity in man. The most prominent one is called BOLD, and is based on the fact that blood flow increases way past what is needed with increased brain activity. This was actually noted by Wilder Penfield operating on the brain for epilepsy in the 30s. When the patient had a seizure on the operating table (they could keep things under control by partially paralyzing the patient with curare) the veins in the area producing the seizure turned red. Recall that oxygenated blood is red while the deoxygenated blood in veins is darker and somewhat blue. This implied that more blood was getting to the convulsing area than it could use.

BOLD depends on slight differences in the way oxygenated hemoglobin and deoxygenated hemoglobin interact with the magnetic field used in magnetic resonance imaging (MRI). The technique has had a rather checkered history, because very small differences must be measured, and there is lots of manipulation of the raw data (never seen in papers) to be done. 10 years ago functional magnetic imaging (fMRI) was called pseudocolor phrenology.

Some sort of task or sensory stimulus is given and the parts of the brain showing increased hemoglobin + oxygen are mapped out. As a neurologist, I was naturally interested in this work. Very quickly, I smelled a rat. The authors of all the papers always seemed to confirm their initial hunch about which areas of the brain were involved in whatever they were studying. Science just isn’t like that. Look at any issue of Nature or Science and see how many results were unexpected. Results were largely unreproducible. It got so bad that an article in Science 2 August ’02 p. 749 stated that neuroimaging (e.g. functional MRI) has a reputation for producing “pretty pictures” but not replicable data. It has been characterized as pseudocolor phrenology (or words to that effect).

What was going on? The data was never actually shown, just the authors’ manipulation of it. Acquiring the data is quite tricky — the slightest head movement alters the MRI pattern. Also the difference in NMR signal between hemoglobin without oxygen and hemoglobin with oxygen is small (only 1 – 2%). Since the technique involves subtracting two data sets for the same brain region, this doubles the error.

Does anyone in China want to go back to the ’80s?

The following is an abstract of an article in PNAS appearing in the 13 May’14 issue (full reference below). The authors are Yu Xie and Ziang Zhou from Peking University and the University of Michigan (respectively). Much is made of income inequality in the USA and what a terrible thing it is. Fortunately for those of the left who find this distressing, there are still a few places left with true equality of income. Cuba comes to mind. Res Ipsa Loquitur.

“Using multiple data sources, we establish that China’s income inequality since 2005 has reached very high levels, with the Gini coefficient in the range of 0.53–0.55. Analyzing comparable survey data collected in 2010 in China and the United States, we examine social determinants that help explain China’s high income inequality. Our results indicate that a substantial part of China’s high income inequality is due to regional disparities and the rural-urban gap. The contributions of these two structural forces are particularly strong in China, but they play a negligible role in generating the overall income inequality in the United States, where individual-level and family-level income determinants, such as family structure and race/ethnicity, play a much larger role.

Since its beginning in 1978, China’s economic reform has led not only to rapid economic growth but also to a large increase in economic inequality. Although scholars continue to debate about precise estimates (1), the consensus is that income inequality in China has now reached a level much higher than that in the United States (2). As we will discuss below, the Gini coefficient for family income in China has now reached a level above 0.5, compared with 0.45 in the United States in 2010. This finding is significant because China had a very low level of income inequality as recently as in the late 1980s (3). Ordinary persons in China know about this increase, as they have personally experienced it in their own lives (4). Although ordinary Chinese people seem to tolerate the high inequality (4⇓–6), they also recognize it as a social problem needing to be addressed. In fact, out of a number of social issues given, respondents in a 2012 national survey rated economic inequality (more precisely, the “rich-poor gap”) the most severe, above corruption and unemployment (7).”

[ Proc. Natl. Acad. Sci. vol. 111 pp. 6928 - 6933 '14 (Issue of 13 May '14) ]

Why marihuana scares me

There’s an editorial in the current Science concerning how very little we know about the effects of marihuana on the developing adolescent brain [ Science vol. 344 p. 557 '14 ]. We know all sorts of wonderful neuropharmacology and neurophysiology about delta-9 tetrahydrocannabinol (d9-THC) — http://en.wikipedia.org/wiki/Tetrahydrocannabinol The point of the authors (the current head of the Amnerican Psychiatric Association, and the first director of the National (US) Institute of Drug Abuse), is that there are no significant studies of what happens to adolescent humans (as opposed to rodents) taking the stuff.

Marihuana would the first mind-alteraing substance NOT to have serious side effects in a subpopulation of people using the drug — or just about any drug in medical use for that matter.

Any organic chemist looking at the structure of d9-THC (see the link) has to be impressed with what a lipid it is — 21 carbons, only 1 hydroxyl group, and an ether moiety. Everything else is hydrogen. Like most neuroactive drugs produced by plants, it is quite potent. A joint has only 9 milliGrams, and smoking undoubtedly destroys some of it. Consider alcohol, another lipid soluble drug. A 12 ounce beer with 3.2% alcohol content has 12 * 28.3 *.032 10.8 grams of alcohol — molecular mass 62 grams — so the dose is 11/62 moles. To get drunk you need more than one beer. Compare that to a dose of .009/300 moles of d9-THC.

As we’ve found out — d9-THC is so potent because it binds to receptors for it. Unlike ethanol which can be a product of intermediary metabolism, there aren’t enzymes specifically devoted to breaking down d9-THC. In contrast, fatty acid amide hydrolase (FAAH) is devoted to breaking down anandamide, one of the endogenous compounds d9-THC is mimicking.

What really concerns me about this class of drugs, is how long they must hang around. Teaching neuropharmacology in the 70s and 80s was great fun. Every year a new receptor for neurotransmitters seemed to be found. In some cases mind benders bound to them (e.g. LSD and a serotonin receptor). In other cases the endogenous transmitters being mimicked by a plant substance were found (the endogenous opiates and their receptors). Years passed, but the receptor for d9-thc wasn’t found. The reason it wasn’t is exactly why I’m scared of the drug.

How were the various receptors for mind benders found? You throw a radioactively labelled drug (say morphine) at a brain homogenate, and purify what it is binding to. That’s how the opiate receptors etc. etc. were found. Why did it take so long to find the cannabinoid receptors? Because they bind strongly to all the fats in the brain being so incredibly lipid soluble. So the vast majority of stuff bound wasn’t protein at all, but fat. The brain has the highest percentage of fat of any organ in the body — 60%, unless you considered dispersed fatty tissue an organ (which it actually is from an endocrine point of view).

This has to mean that the stuff hangs around for a long time, without any specific enzymes to clear it.

It’s obvious to all that cognitive capacity changes from childhood to adult life. All sorts of studies with large numbers of people have done serial MRIs children and adolescents as the develop and age. Here are a few references to get you started [ Neuron vol. 72 pp. 873 - 884, 11, Proc. Natl. Acad. Sci. vol. 107 pp. 16988 - 16993 '10, vol. 111 pp. 6774 -= 6779 '14 ]. If you don’t know the answer, think about the change thickness of the cerebral cortex from age 9 to 20. Surprisingly, it get thinner, not thicker. The effect happens later in the association areas thought to be important in higher cognitive function, than the primary motor or sensory areas. Paradoxical isn’t it? Based on animal work this is thought to be due pruning of synapses.

So throw a long-lasting retrograde neurotransmitter mimic like d9-THC at the dynamically changing adolescent brain and hope for the best. That’s what the cited editorialists are concerned about. We simply don’t know and we should.

Having been in Cambridge when Leary was just getting started in the early 60’s, I must say that the idea of tune in turn on and drop out never appealed to me. Most of the heavy marihuana users I’ve known (and treated for other things) were happy, but rather vague and frankly rather dull.

Unfortunately as a neurologist, I had to evaluate physician colleagues who got in trouble with drugs (mostly with alcohol). One very intelligent polydrug user MD, put it to me this way — “The problem is that you like reality, and I don’t”.

A Touching Mother’s Day Story

Yes, a touching mother’s day story for you all. It was 47 years ago, and I was an intern at a big city hospital on rotation in their emergency room. The ER entrance was half a block from an intersection with a bar on each corner. On a Saturday night, we knew better than to try to get some sleep before 2AM or until we’d put in 2 chest tubes (to drain blood from the lungs, which had been shot or stabbed). The bartenders were an intelligent lot — they had to be quick thinking to defuse situations, and we came to know them by name. So it was 3AM 47 years ago and Tyrone was trudging past on his way home, and I was just outside the ER getting some cool night air, things having quieted down.

“Happy Mother’s day, Tyrone” sayeth I

“Thanks Doc, but every day is Mother’s day with me”

“Why, Tyrone?”

“Because every day I get called a mother— “

Help wanted

Just about done with special relativity. It is simply marvelous to see how everything follows from the constancy of the speed of light — time moving more slowly for a moving object (relative to an object standing still in its own frame of reference), a moving object shrinking (ditto), the increase in mass which occurs as an object begins to approach the speed of light, and how this leads to the equivalence of mass and energy. Special relativity is even sufficient to show how a gravitational field will bend light — although to really understand this, general relativity is required.

The one fly in the intellectual ointment is the Minkowski metric for the space time of special relativity. In all the sources I’ve been able to find, it appears ad hoc, or is defined analogously to the euclidean metric. I’d love to see an argument why this metric (time coordinates positive, space coordinates negative) must follow from the constancy of the speed of light. It is clear that the Minkowski metric is preserved under the hyperbolic transformation of space-time, but likely others are as well. Why this particular metric and not something else.

Consider the determinant function of an n by n matrix. It has a god awful mathematical form involving the sum of n ! terms. Yet all you need to get the (unique) formula are a few postulates — the determinant of the identity matrix is 1, the determinant is a linear function of its rows (or its columns), interchanging any two rows of the determinant reverses the sign of the determinant, etc. etc. This basically determines the (unique) formula of the determinant. I’d really like to see the Minkowski metric come out of something like that.

Can anyone out there shed light on this or give me a link?

Follow

Get every new post delivered to your Inbox.

Join 66 other followers