Coming to Terms with Blogging
Blogging on one’s own website is sad enough, but worse still I am replying to my own blog. Nobody else will – my blogs haven’t attracted a single comment in over a year. Could that be because they are exceedingly dull?Yet I have to admit I have changed my mind about blogging, which is my reason for replying to myself. As you can see, I saw blogging as a witless activity pursued by literary masturbators for consumption by idle surfers too lazy to seek out the really great waves of enlightenment sweeping distant oceans of truth. Blogging I thought was rather as the Irish comic writer Flann O’Brien once said of poetry, that is not intrinsically bad, but corrupted by the dead weight of hopeful human mediocrity. “For every good poem there are 1000 bad,” O’Brien once complained in the Irish Times. Applied to blogging you would have to add at least two noughts to his ratio.
But now, 18 months older and a not a little humbled, my opposition to blogging has softened. Perhaps that is because I am catching the affliction, but what I once saw as unpaid self flagellation, I now see as free advertising for the enterprise of one’s intellect. Like the web as a whole, the blogosphere is a Darwinian jungle of ideas. It may seem to trumpet the commonplace, but it does not, as is sometimes erroneously believed democratise success. The simple law of numbers ensures that - if every man and his dog is blogging then most of them are whistling in the dark. But the web does democratise the gateway to success, patrolled by the blogosphere’s own unappointed thought police.
End
Irrational numbers are singularities
I have for long been troubled by the idea of irrational numbers, and by corollary uncountable numbers. The set of all irrational numbers is uncountable, if it exists. That caveat will recur throughout this blog, and a quick google of the words irrational numbers existence will reveal that I am not alone in this concern.Firstly just a few definitions. A set of numbers is countable if it is “like” the integers or whole numbers 1,2,3 etc, in the sense that it can be mapped in some 1-1 correspondence with them. That is to say a set is countable if there is way of counting through them one after the other such that any specified member of the set can be reached in a finite number of steps, even though the set may go on for ever.
Rational numbers are all fractions of whole numbers, and they too are countable, even though they appear to be more numerous than the integers. Indeed between any two integers such as 1 and 2, and for that matter any two fractions such as 7/11 and 8/11, there are an infinite number of other rationals. Yet the fractions can be counted as follows: 1/1, ½, 2/1, 1/3, 2/2, 3/1, ¼,2/3,3/2, 4/1 etc. This scheme counts the number one indefinetly, but at least it is guaranteed to reach any fraction M/N in a finite number of steps, whatever the values of M and N.
Many numbers can be proved irrational, if they exist. Well known examples are the square root of 2 (and any rational number except those whole numerators and denominators are both perfect squares), and ה All that can actually be shown is that these supposedly irrational numbers generate infinite sequeneces of rational numbers that approximate ever more closely to the target. We can zoom in for example on √2. 1.4 is close, 1.41 is closer, 1.414 closer still and so on. The answer can be computed ever more accurately to a growing number of decimal places given an ever more powerful computer. But there will always come a point when the next decimal place cannot be known, and indeed irrational numbers such as √2 will never be computed exactly in any computable number system, which must involve rational numbers for calculations to be possible. Ultimately √2 can only be expressed as, well, √2, and the same applies to π and the so called transcendental numbers that make up another category of the irrationals, that is to say those that are not roots of polynomial equations whose coefficients are rational numbers, if they exist.
Now consider this. For uncountability to work, we have to assume that you can compare two objects each with an infinite number of components with no recurring patterns. For example the set of all sets of integers is considered to be uncountable, but it can in fact be shown to be countable once we realise that any actual set that is capable of definition can only have a finite number of integers in it, even though there is no limit on this number.
You can have members of the set with an infinite number of integers, but only if there is a repeat – or else how do you define what the member is. If all members of the set end up repeating, then the set is countable.
There is a way out of this conundrum I think. The irrational and rational numbers are both subsets of the real numbers, if they exist. The set of real numbers is the complete plane of continuous numbers, intuitively defined by ruling an infinite continuous line either side of zero. It is an analogue concept, assuming that numbers are generated along a continuous line with no break, and we can see for example that if we start at 1 and move towards two we must pass an imaginary point on that line that equates to every single number, including irrationals such as the square root of two, as well as all rational numbers between 1 and 2 such as 3/2. But the concept of real numbers within a continuous plane is itself a construct of the human mind, with no evidence of its existence in the “real” universe. But all the rational numbers within the real numbers definitely do exist, and the irrationals do define infinite sequences of irrationals that approach ever more closely to these imaginary points. As such I think that the irrationals are best defined as singularities within the real number plane of numbers – unreachable but acting as magnets attracting rational numbers in their vicinity into infinite sequences that approach ever more closely, yet never quite make it.
Blog
I must say at the outset that I am not a great fan of blogging. I am reminded of Samuel Johnson’s view that anyone who writes except for money is a fool, and not much I read in other people’s blogs refutes this. Nearly all the good writing I encounter has earned money in some way for its creator. There are it is true some good blogs out there, but finding them is about as hard as it would be to locate great poetry by digging amongst all the doggerel that has ever been written.I will therefore blog sparingly. This is no guarantee of quality, but hopefully I will avoid verbal incontinence and at least keep my outpourings terse and to the point.
My first blog expresses my despair at the course of the global warming debate, which has arrived at a so called consensus. The theoretical case for urgent action is I agree overwhelming, and on the whole I am not against the steps being taken, even if some of them seem motivated by hysteria or excessive ecological zeal, rather than the real contribution they are likely to make to reducing atmospheric carbon levels. The faith in wind farms in particular seems misplaced, except as a source of power for remote sparsely regions, or for individual homes in windy locations, but not to supply major population centres. The future lies in solar energy conversion, either via artificial photosynthesis, or from plants engineered to produce hydrogen or possibly even hydrocarbons rather than carbohydrates. Research into nuclear fusion should also continue.
Yet the evidence that humans have already contributed substantially to a warming planet does not stack up, at least not just yet. While some warming has been observed in some parts of the planet, notably western and central Europe, the climate models fail to account for various anomalies that have been observed, such as a slight cooling over a large part of the Antarctic continent over the last two decades. The models have consistently predicted that the Polar Regions would exhibit the earliest and strongest response to anthropomorphic production of greenhouse gases, and this is evident only in the Arctic, and even there with some exceptions. Until the climate forecasting models account accurately for the present situation, they cannot be trusted on their own as sources of evidence for major changes in energy policy. The models need to be upgraded to take account of important inputs to weather and climate that are currently ignored, such as high energy particles striking the atmosphere from the sun and outer space. Such particles exert an influence out of proportion to their total energy by affecting the formation of clouds and thunderstorms that in turn have a more significant affect on the global radiation budget. In other words their affect is amplified by the global weather system. Incorporating these and some other factors will also lead to more accurate medium range weather forecasts over the 5 to 12 day period.
Aerosol Ignorance
Why is it that I find blogging so repulsive and repellant that I have not done any for six months, in fact since my web site went live? During that time I have written well over 100,000 words as a journalist, and earned good or bad money for it. Could it be that I am washed out and do not have an interesting thought in my head? Yet some of the most prolific bloggers are professional journalists more fecund than I, and they tend to be more interesting than the hordes of amateurs sinking in the morass of published anonymity that accounts for much of the World Wide Web. Blogging is supposed to fulfill that insatiable human desire to communicate, but in truth it is a staircase leading to a spiritual wilderness, save for the chosen few whose words have a regular audience and would probably be read or heard anyway. Blogging imposes no constraint of space, thereby encouraging turgiversity, although the best instances of it are trimmed by the exigencies of time.
Having got that off my chest, my spirit can breathe more easily, and I even feel up to a little blog at last. Inevitably my thoughts turn to plastic bags and tungsten light bulbs. I have become a hoarder of both, terrified that within two years I may not be able to procure either. I am of course only too happy to save money on energy, but I resent the heavy weight of the state driven by environmental fascism, or should I say communism, behind over hasty token gestures.
I am accused of being a global warming skeptic, but I am merely skeptical of current climate forecasting models. I am all for a coherent move away from fossil fuels to sustainable alternatives, but panic is pointless because the current forecasting models are virtually useless, failing to take proper account both of the huge role of aerosols, and long term ocean circulation, in weather and climate change. In fact cosmic rays, which trigger aerosol formation by ionizing particles in the atmosphere so that they grow by electrostatic attraction, are not even included in the present models. To be fair there is great ignorance over the link between aerosols and climate via their role as condensation nuclei, although this means there is so much uncertainty that climate experts, in private at least, admit that it is not even clear whether anthropomorphic greenhouse gas production will lead to warming or cooling over the next 50 years, and can only say that the former is more likely.
Even if the models were correct, an over-hasty response is still likely to have more downsides than benefits. We need to increase budgets for long term research into solar energy conversion, and possibly nuclear fusion, while ending this futile flirtation with wind power, which, shackled by the laws of physics, is a pox upon our land and sea scapes.