Carrock

In "2" you say "Because the intervals are always empty when n→∞, the set of all fractional binary numbers is not continuous but discrete" I suspect you implicitly mean by n→∞ that n is or becomes larger than any given finite number but n is still finite. You then have 2^n +1 discrete points which maps to a subset of the rational numbers. Only if n=aleph-null are all the real numbers (from 0 to 1) represented and there are are then no intervals between numbers. I agree that "binary numbers has the same cardinality as the real numbers" but by keeping n finite you are only listing a countable, finite set. You can create an aleph-null set of real binary numbers by mapping to eg an infinite set of integers. You can create from that set an aleph-one set using Cantor's diagonal method. I think all real numbers can expressed as a binary or decimal mixed number or mapped to a finite range of values eg 0 to 1. pi eg can be expressed in decimal or binary but it's not a countable number. tnx pengkuan: this was a useful learning experience for me and I hope you.

I was just pointing out specific errors. I looked at your second link and while it appeared to be accurate, I think it's pretty well impossible to use it for learning. You might find this refutation, using transfinite maths, of the possibility of an eternal expanding universe Philosophy of Science Vol. 32, No. 1 (Jan., 1965), pp. 21-31 interesting. (free registration on site required to read it) It's very clearly written as many people resist transfinite maths' concepts. One 'expert' here knew its conclusions were wrong without even reading the abstract.

An infinite quantity of pure gold contains no silver. There is an infinite range of frequencies in the visible light spectrum; the number of colours is a lot less (or more) than 16,000,000 as colour is subjective and eyes cannot distinguish that many. Main problem: where on the canvas is the picture of the entire canvas?

I suspect most professional hackers no longer support XP hacks. Free antivirus seems entirely adequate to block attacks. As there is around a ten minute window between Microsoft removing enough bugs for an OS to be usable and ending support for the OS I only upgrade when I have to. I have tried 10 or 11 on a friend's rarely used computer for software whose main enhancement is XP incompatibility. I enjoy a leisurely toast and coffee while it's booting and installing upgrades and rebooting and giving and sometimes cancelling security warnings.

A quote from http://sharpagain.org/how-a-doctor-reversed-her-husbands-alzheimers-disease-in-37-days:

According to NASA, this one is genuine.

My 'problem' with you is the usual one - you expect people to have faith in you. You not only claim not to have used the term 'negative vacuum,' you quote 'negative vacuum' again in your next post. You could not make it clearer that you expect uncritical faith that you are right. Clearly moderator swansont has faith in you and I am probably outnumbered, which is a sad way to end a discussion on a forum with 'science' in the title. As you ignore any criticism you can't refute, this is my last post.

In this thread 'Mordred said 'You can however have negative vacuum' and corrected it to 'A vacuum is a pressure terminology' I don't believe you can usefully define vacuum as equal to one of its propertties. In his OP he said in effect that vaccuum is a number. That was his '1=2 thefor...' moment. If Mordred had read about eg negative gauge pressure and then said 'negative vacuum' and then in a later post confirmed (approx) that vacuum is sYnonymous with pressure I would describe that as a new definition probably created by Mordred's failure to understand the relevant science. I know (just) enough about vacuum energy to know when I'm reading rubbish; all Mordred's OP does is provide misinformation.

I was hoping for a clarification, not an explanation of how you are ascribing an unhelpful new definition to an old term. A few points to consider before reusing your new definitions in public: Air pressure as generally understood seems to fit quite well your definition of vacuum. Must all future measurements of air pressure (sorry pressure terminology) include its expansion/contraction rate or will you define air pressure as a new sort of pressure terminology? As vacuum has been preempted, will the volume aspect of space in future be defined as 'space is a volume terminology'? And so on.... I know you regard science on this site which has not been published in a journal or similar as suitable only for the the trash can but perhaps you have been so busy searching out such posts that you have not had time to apply similar standards to yourself. I usually stop reading your posts when I come across the equivalent of '1=2 therefor...' but on this occasion perhaps you deserve the sort of help you give many other people.

I don't understand how a vacuum can somehow be less than nothing. Please explain.

How was a photon observed to be moving slower without observing its behaviour? Saying it slows down because the photon can be treated as a continuous classical wave interacting with a not very classical continuous electron wave can give correct answers to a high degree of accuracy. No doubt this is one reason Newton's belief that light was composed of particles was rejected for some centuries. Zap your glass with gamma rays and as you increase the energy you can make each interaction occur in an arbitrarily small volume. (The gamma ray is the pre QM 'passive observer'). Has QM proven that photons travel at variable speed? You may be thinking of observing these photons using a short wavelength low energy electromagnetic field. Einstein's Nobel prizewinning paper on the photoelectric effect demonstrated you can't do this. The wavefunction of the field of the photoelectric photon could be 1/100th mm or a mile in diameter before the interaction. No way to tell and this experiment cannot be explained if light is not quantised. Using electron(s) in a double slit experiment you see an interference pattern provide you don't observe the interaction. Similarly you can calculate that eg a photon has a 10% chance of interacting with a field a ( or do you mean particle a?) and 3% with field b. IF you observe with a photon or particle you will affect it so much that you could say it has eg a 99.99% chance of interacting with a and a 3% (or so) chance of interacting with b. ie interactions do not localise particles until they are observed.

Some of the early A.M. transmitters used carbon microphones (as used in telephones) to modulate the carrier so it's not just theory!

The topic title is "A Steady State Universe". Unlike Steady state cosmology, my version has certain values set such that it is past and future complete. I presume you're referring to eternal inflation I could provide a similar quote from most papers on inflation. Is the value of such inflation theories a function of how many people have demonstrated that with certain assumptions, they predict eternal inflation? I didn't know, let alone understand any of the models you cited. There was one which I managed to work out by searching for "1090". Perhaps you will tell me if I got it right. Again in eternal inflation I presume you are stating that there are no particles ( and no space ) anywhere except in the visible part of the universe and no more will ever be created. This seems rather improbable but would certainly make inflation future complete. I wonder if you actually read my original post. I gave two important reasons that the Hoyle steady state universe was untenable; you state the ( Hoyle ) steady state universe has been proven wrong ( which I agree with ) as inflation has been observationally proved(!!!!) A brief (over?)simplified resume of my theory: Finite inflation is initiated in flat, past and future complete static Minkowski space. Most models of inflation are past incomplete and are consistent with this or a similar origin. Only finite inflation is permitted as no future incomplete processes are possible in a future complete universe. Therefor the inflation episode we're living in will end completely in less than a very long but finite time. Over long enough time and distance, this future complete static Minkowski space is unchanging, exactly as the BGH steady state universe was unchanging. A property of the static Minkowski space I use is that its temperature is asymptotically zero degrees so Olber's paradox is no a problem.

Mordred, michel123456, swansont et ( I hope ) al : Thank you for responding to my post. The "Steady State Universe" I referred to is and also asymptotically zero temperature. In my theory, our observable ( pocket) universe is a result of finite inflation from this steady state universe much as described in eg Eternal inflation and its implications: Except possibly for subtle CMBR variations my theory does not require any variation in the observable universe from predictions in other inflation theories (but is incompatible with theories requiring future-incomplete eternal expansion). Therefor the posts about the CMBR background are not really relevant to this theory. For brevity and laziness, there are a lot of implicit assumptions in my original post; some of them 99% of cosmologists would agree with, others not. I'd be happy to defend or abandon assumptions anyone on the forum finds dubious.

So many crackpots try and defend that idea, it is a bit cliched. We need someone to revive phlogiston. I can't revive every idea but if dephlogisticated air was good enough for Priestley it's good enough for me... Monday was rather optimistic.... A brief preemptive defense... This post Steady state cosmology, proposed by Sir James Jeans and later revised by Fred Hoyle, Thomas Gold, Hermann Bondi and others, postulated an eternal, exponentially expanding universe with matter creation such that the average matter density was always constant. This theory was effectively refuted observationally by the discovery of cosmic microwave background radiation (CMBR) in 1965. There was also a serious problem with this theory which did not affect its verifiable predictions but dealt a fatal blow to the 'steady state' description:- If it is assumed that at some past time the universe had a countably infinite ( ie aleph-null ) volume and number of discrete particles, and expansion continued for countably infinite time, the volume of space and the number of particles in it become uncountably infinite. That is, the volume and number of particles increases by the factor n^aleph-null, where n>1. Since n^aleph-null is equal to aleph-one, the volume of space and the number of particles in it would become equal to the uncountable ( or non-denumerable) infinity aleph-one, which is physically impossible. At least, I am not aware of any way it could be possible. A detailed and rigorous analysis of the problem is presented by Richard Schlegel in Philosophy of Science Vol. 32, No. 1 (Jan., 1965), pp. 21-31 Before observational refutation, Steady state cosmology could only be kept viable by assuming exponential inflation started at an indefinitely distant but finite time in the past and will end at an indefinitely distant but finite future time. ie, more formally, exponential inflation must be past-incomplete and future-incomplete. The same problem occurs with a newer theory of an eternal, exponentially expanding universe ie eternal inflation which also predicts exponentially increasing space and number of particles. Such future-incomplete expansion is often described by cosmologists as 'eternal to the future', a convention which I will adopt. Cosmology is a science where many competing theories can survive because confirming or refuting them is difficult or impossible. I have a subjective preference for theories which are past- and future- complete and do not require the universe to be finite. One possibility which has been somewhat neglected is an eternal steady state static universe with finite inflation and a concept originated by Dr. Schuetz: The specific aspect which I feel has been neglected is that in an eternal universe no eternal process ( not necessarily inflationary ) which requires the creation of space or discrete particles can ever be initiated. My steady state 'update' is not up to the old steady state theory in falsifiability, but it is incompatible with some respected theories and may soon make the trip to 'Speculations'. I assume an eternal ( ie past and future complete ), flat, static, spatially infinite universe which, on a large scale, has asymptotically zero energy and maximum entropy ie Minkowski space. I will follow precedent and call 'local' universes like ours 'pocket universes'. As eternal or finite inflation theories are the most consistent with the observed CMBR, I will use finite inflation in my theory. It is then necessary that there be a nonzero possibility of inflation and it is convenient and perhaps necessary to assume that the probability of producing Boltzmann Brains ( an awkward prediction of many theories ) is much lower than the probability of inflation. In Can the universe afford inflation? Andreas Albrecht and Lorenzo Sorbo propose that this is a viable assumption. There is a ( small ) possibility that ongoing observations of the CMBR will support this theory. Its main value, if any, is that some well regarded theories' predictions are incompatible with this theory. Therefor, in this post, rather than make predictions consistent with other theories I will only consider predictions of theories which are inconsistent with this theory. The most important constraint of this eternal universe theory, which does not apply to most theories, is that to avoid slow, exponential inflation of the universe it is necessary for everything created by an instance of inflation to disappear completely within finite time. That is:- Within finite time, each instance of inflation must end and all created space, particles and other entities eg singularities must disappear. This may take a very long time - eg the half-life of the proton is greater than 10^33 years. From this it follows that the pocket universe we live in ( and everything created by inflation ) cannot expand eternally to the future, but there need not be any presently detectable way for it to disappear. All models where quintessence, cosmological constant etc cause such expansion are not viable. As the expansion of space during inflation is finite, after sufficient time has elapsed, all created space must eventually be separated by time-like intervals. This should lead to the complete disappearance of everything created by the inflation episode. If, as is certainly plausible, new instances of inflation can start within an inflation field or pocket universe, finite inflation requires on average less than one in each new instance of inflation. ( Otherwise inflation would be eternal to the future.) An adaptation of reasoning regarded as dubious by Alan H. Guth: If finite inflation is assumed to have an exponential phase, it is likely our universe was created around the time of peak creation of universes when inflation was about to end; there may possibly be some trace of this in the microwave background. If it is possible for intelligent life to initiate inflation, this sets a further constraint on the probability of any single inflation episode producing intelligent life. If on average each instance of intelligent life creates x new inflation episodes, then all inflation episodes must on average produce less than 1/x instances of intelligent life. if this is the case, the total duration of inflation is further limited and there is a slightly better chance of observing transients dating back to the inception of inflation. I suggest one other constraint for finite inflation in an eternal universe, which is that its finiteness must not depend on carefully selected parameters. In an eternal universe the probability of eternal inflation must be 0. Finally there are so many extant theories I can only hope that I am not repeating one of the more obscure ones......

Good loft insulation.

I am certain you are not a skeptic

There is quite a lot of useful information here: https://www.physicsforums.com/threads/magnetic-force-inverse-cubed-law.587204/

Fred Hoyle's steady state universe is overdue for revival. I'll try to have something up for Monday.

No need to quote a poet...... Winners of the Ig® Nobel Prize 2000 PSYCHOLOGY: David Dunning of Cornell University and Justin Kruger of the University of Illinois, for their modest report, "Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments." [Published in the Journal of Personality and Social Psychology, vol. 77, no. 6, December 1999, pp. 1121-34.]

You mention a hypothesis that seems very like hormesis and clearly consider this to be a reasonable hypothesis and not pseudoscience. I'm not clear what you are arguing for. I suspect benign radiation induced DNA changes are swamped by the malign changes. The jury is still out on this. A couple of quotes from the original source of that quote indicative of its quality:

From the Wikipedia article ( http://en.wikipedia.org/wiki/Radiation_hormesis ) Strange cited: Strange: Do you have faith in totally error-free DNA repair or do you think damaged DNA is harmless or even benign? Perhaps you were referring to this study of the effects of a widespread accidental exposure to cobalt-60. I don't think you were referring to this later publication on the same incident, quoted in the Wiki. or this : As you seem to claim this Wiki has peer reviewed science supporting hormesis perhaps you would would specify where this can be found on the Wiki. I couldn't find anything that wouldn't be relegated to "Speculations" if it were presented as research on this forum. [edited for minor errors.]

I can't give any better answer than in my previous post.

'which way the conventional current flows through the capacitor' As (ideal) capacitors don't pass direct direct current the answer is ( at different times ) left to right, right to left and there is no current at all. 'ie which direction is the direction of conventional current around loopABCD' As current (and its direction and phase) varies around the loop (it may or may not change direction through CD) I can't answer this question or understand how it is the same as asking 'which way the conventional current flows through the capacitor' 'Now reverse the power supply to the resistor chain, as in fig2 and answer the same question.' After transients have become negligible the answer is as above. Was this a trick question?