Ada Lovelace and the Konigsberg Bridge problem

The Weston Library had a display about Ada Lovelace. She is regarded as the first computer programmer. She was a friend of Charles Babbage who designer the first calculating machine and she is credited with writing the first algorithm for a machine like that.

I was interested to see the Konigsberg Bridge problem mentioned. I remember hearing about it when I was at school. Essentially it is a question of whether you can cross seven bridges once in a single journey as they were laid out in the town of Konigsberg. https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg You can read about how Leonard Euler proved it was impossible. It brings up the mathematical concept of "graphing" -  ie drawing networks. I have posted about this before when dealing with knots.

Embroidered referencing in the New Bodleian

What was the New Bodleian has been turned into the Weston Library with exhibition space and a cafe.To mark the 800th anniversary of the Magna Carta, someone decided to embroider the whole Wikipedia page on the subject. It's huge. What I love about Wikipedia is the way that it is well-referenced. I have been trying to teach my classes to include (date accessed) when referencing web pages. This is important because unlike printed material, they can change.

Is the reflected light still quantised?

I was going to post about low energy bulbs giving out quantised light rather than a full black body spectrum like a filament bulb. The reason is because high energy electrons are fired through a gas in the bulb. The electrons hit the gas atoms. This provides energy to knock different electrons that are bound within the atoms. The bound electrons jump up energy levels and then de-excite, emitting photons of light but only at the frequencies permitted by the electron level jumps. So you get a spectrum with discrete frequencies. I took this photograph with a diffraction grating to illustrate this point. But looking at it, the coloured part is the light from the lampshade - reflected light. It is from a white surface so it is likely to be the same as the bulb, but might it not tend back towards a full spectrum? Need to think about this.

Stripy clouds over Wigton

 I spotted this stripy sky over Wigton this morning - the sort of cloud formation that made me do a lot thinking in the summer. Then I remembered an experiment from the old Nuffield Physics A Level course. Stick a knife blade high up under the narrow flow from a tap and you get a stripy pattern too.

For the tap, it is a stationary wave. At least that's what the book says. For a stationary wave, an incident wave hits an obstacle and bounces back. The incident and reflected waves interfere. Not quite sure where the wave is originally because it's just a column of water. Anyway, it occurred to me that with the clouds, one moving air mass could be hitting another more stationary air mass to replicate the knife scenario...?

"Bad Greenhouse"

A colleague pointed out this website to me: http://www.ems.psu.edu/~fraser/Bad/BadGreenhouse.html I'm interested in getting to the bottom of this. I was taught (back in the days when the next Ice Age was being predicted so before any idea of a runaway Greenhouse Effect) that a greenhouse works because light from the Sun at short wavelengths can get through the glass. These are absorbed and heat the contents. The contents are now warm but not as warm as the Sun, so they now emit at longer infra-red wavelengths which can't get through the glass. I had heard rumours that there might be problems with this. The linked webpage talks about the glass stopping convection. That's undeniably true. I'm really interested in the idea that the atmosphere radiates electromagnetic waves like a star. I've never heard that said before but it's utterly logical. For any black body (the name given in Physics to a perfect emitter of electromagnetic waves (remember that matt black painted objects cool faster..) Wien's Law applies: wavelength of peak emission intensity x absolute Temperature = a constant. So the colder the object is, the longer the wavelength, from my original teaching. But the idea that this could heat the Earth's surface more than the Sun is new to me and may be worthy of some calculations... Hopefully more to follow.

Looking back in Wigton car park

The inside rear view mirror is a plane mirror. It shouldn't distort the object. Theory says that the virtual image (the picture in the mirror) should be the same distance behind the mirror as the object is in front. In other words, it should show true distances. The driver's door mirror is convex. This gives a wider field of view but the image appears further away.

Starlings in ultra-violet

Here's a Starling on Mrs B's garden feeders. Male and female Starlings look identical to me. So how do they decide who is a girl and who is a boy? It turns out that the female Starlings have patches of ultra-violet on their heads. You need to think of ultra-violet as a different - just one that we can't see. It's counter-intuitive - a colour that you can't even imagine. But Starling eyes can see those frequencies. I wonder what it looks like? When we "see" ultraviolet or infrared, they are done as FALSE COLOUR images. Get it explained properly by watching this awesome programme soon whilst it is still on the iplayer http://www.bbc.co.uk/iplayer/episode/b06pm7t8/colour-the-spectrum-of-science-3-beyond-the-rainbow

Filament light bulbs

I found these clear glass filament bulbs in a tea shop with a retro feel. This is what the first sorts of light bulb looked light. The idea was to put a high enough current through a strip of conducting wire to make it glow without burning. The bulb contains an inert atmosphere so no oxygen can get in to react. If it did, the filament would burn away quite soon. Carbon was the first to be used - remember that graphite conducts. I have no idea whether these are carbon, platinum or tungsten, which was the most commonly used. Too much thermal energy was being produced by this type of bulb for each unit of light produced - but clearly not enough thermal energy to heat your room. It was wasted and so made the bulbs less efficient. This is why they have been replaced by the small fluorescent tubes.

A primitive rain gauge

Mrs B came up with the idea of using a weighted bucket as a primitive rain gauge to measure the weekend's deluge. This is what we made on Friday. The sides of the bucket are almost straight-sided. It would be important for the hole at the top to have the same area as the bottom. I put the cover on to stop leaves and stuff like that blowing in. The rocks are to stop it blowing away in the gales. I lifted them out to measure. It collected 60mm over 12 hours on Saturday night - that's wet. It is very open and could be susceptible to evaporation problems in strong wind and strong sunshine. I should work on a more conventional design.

Trying to estimate the rainfall

It has been raining hard in Cumbria this weekend. They were predicting up to 250mm. That certainly hasn't happened in Wigton but when we drove down to Keswick today it was very wet. I'd estimate that Derwent Water was about a metre up on normal. Here are some pictures:

The lake is fed from the streams that come in from the hills. Any land that feeds a stream going into Derwent Water is its catchment area. From the map, I'd estimate the catchment area as perhaps 14km x 7km making an area of about 100 square km to 1 significant figure. Estimating the lake as 4km x 2km gives it an area of 8 square km. This puts the catchment area as 12 x the lake area. Water in the lake 1m higher would mean a rainfall of 80mm over the catchment. Some of the water would not yet have fallen; some of the water is still flowing down from the hills and some of the water has flowed out towards Bassenthwaite Lake. Even so, 250mm hasn't happened, which is wonderful news. That's what they are saying on the weather bulletins tonight.

Underground cables on the Southern Upland Way

We found a set of underground cable markers on the Southern Upland Way west of Moffat. I went looking for information about how deep they were buried but found this instead http://www.emfs.info/sources/overhead/specific/132-kv/ Click on the "underground" option. I cannot verify this data. Maximum magnetic field strength would be less than 10 microTeslas. The strength of the Earth's magnetic field is between 25 and 65 microTeslas so I don't think the reported reading is significant. I need to take my magnetic field measured if I go again!

Verdünnen Schwerkraft auf meine Physiktasse

Dieses Jahr studiere ich Deutsch. Ich will etwas auf Deutsch schreiben. Ich habe über meine Physiktasse gedacht. Ich sehe, dass die Gewichtskraft zwei Komponenten hat. Eine Komponente ist senkrecht zur Oberfläche. Auf Englisch sagen wir „Normal Reaction Force“. Die andere Komponente heißt die Hangabtriebskraft, die nicht so groß wie die Gewichtskraft ist. Das bedeutet, dass die Beschleunigung des Balls nicht groß ist. Auf Englisch, heißen wir das „dilute gravity“. Die Koordinatenachsen sind senkrecht, aber ich denke wieder über dem Fall, wenn sie nicht senkrecht seien.

Making a loudspeaker

My class made loudspeakers like this. We put alternating current from a signal generator into a coil of wire, which was taped to the back of a paper cone. The coil turns into an electromagnet but with north and south poles that alternate with the current. The coil-electromagnet sits between the poles of a permanent magnet. They alternately attract and repel, which makes the cone vibrate and you get a buzzing noise at the set frequency.

Crooke's Radiometer

I remembered this experiment and it turned out we had it in the cupboard. It's like a 4-paneled weather vane in a partial vacuum. When you shine a light on it, the vane spins. I gave out what I understood to be the explanation, but I was wrong! I said that the momentum of the light photons, calculated by De Broglie's equation, changes on impact with the vanes, so you get an impulse.Thinking about it now, I can see a flaw in my own reasoning. The impulse force would need to create a torque but the light shines equally on both sides as far as I can see. The shiny side would reflect light so there would be a greater change in momentum  and thus a bigger impulse on the shiny side. This would mean it turning anti-clockwise. In fact, it turned clockwise. The real explanation is thermodynamic. I'm still digesting it, but it's here, with a film of it in action https://en.wikipedia.org/wiki/Crookes_radiometer

Change of basis: trying to understand tensors

I've been trying to understand tensors. I have learned that they are a way of doing maths in higher dimensions - that is, going beyond the 3 dimensional world with which we are familiar. The 2D and 3D worlds are subsumed within this framework. And axes do not have to be perpendicular to each other. I've been struggling with that so last night I decided to investigate what happens in 2D. An important thing about the world of tensors is that a given vector must remain unchanged, no matter what set of coordinate axes we are using. They seem to use  the word BASIS to describe the axis set up. So I think my picture above shows a change of basis. The red vector remains the same in each basis but the components of the vector, shown in green, change. I'm working on this because I want to understand the significance of contravariant and covariant factors. I need examples to help my thinking. This post is thinking out loud. They'll be more when I've made progress.

Surface area in the cactus house

This is the Cactus House on the Threave Estate. Notice the extra fins on the heating pipes. I think that the mode of heating is actually by conduction from the metal to the air molecules. This extra energy makes the molecules move further apart, becoming less dense. The less dense air floats up spreading thermal energy by convection. It helps for the pipes to be given an extra large surface area because the thermal energy leaves through the surface. The more surface there is touching the air, the more air can be heated at one go. The cacti employ a different approach. They would lose water through their leaves by evaporation. So the leaves are rolled up into spines to give them a much smaller surface area. Less water vapour is able to escape so they don't dry up. The leaves can't do photosynthesis because they have such a tiny surface area. Hence the stem has to be full of chlorophyll and green so that it can do the photosynthesis.

Olbers' Paradox

 The rain has finally stopped and the sky is clearing. I've just been outside and taken the above photograph of the stars shown on my planisphere below. So why is the sky so black?

Olbers was an 18th Century German astronomer who first hit on the idea that if the Universe was infinitely big and had existed for an infinite length of time, the sky at night should be white. That's because there would by logic be a star in every direction, given even distribution through space. In the infinite time available, light from every direction would have time to reach us. He concluded that the Universe was therefore finite. I had always taken that to mean that it had a limited size, but the stuff I read now seems to suggest that the Universe is infinite in size. But it is finite in TIME. So they now talk about the OBSERVABLE UNIVERSE, the bit from which light has had time to reach us.

Einstein again!

The quotation on the bench probably sums up this blog. I've had a lot of fun so far looking at things and trying to comprehend the Physics. I like the way the seat has been made to look like a wave. Einstein was famous for showing that the speed of light waves in a vacuum is the same no matter who is looking at them.

The spring constant of my knitting

 The blue square is my first completed project with help from Mrs B. Note the change in direction along the diagonal. This helps it to hold its shape better. I used a Newtonmeter to investigate.

 Here's my original knitting with no direction change. It took 3N to stretch it by 9cm. That's 0.33 Newtons per cm which is its spring constant.

Pulling the other way was 1N to stretch 9cm. That's 0.11 Newtons per cm. The spring constant used to be called the stiffness of the material when I studied Engineering. Stiffer materials are harder to stretch. So the knitting is 3 times harder to pull across the rows than along the rows. By having a clever square with rows in perpendicular directions, that difference will be removed and the knitting is equally strong in both directions.

The Butterfly Effect

I photographed this Red Admiral butterfly in our garden during the warm weather a month ago. It reminded of the famous idea that launched chaos theory on the world. In 1963, Edward Lorentz came up with some equations for atmospheric conduction. When plotted in phase space, they resembles the wings of a butterfly. https://en.wikipedia.org/wiki/Lorenz_system His work showed that the weather obeys non-linear relationships - in other words, doubling one thing doesn't often double the other. The response can be quite out of proportion. A small change can produce a big effect. They started saying that if a butterfly flaps its wings in Rio, it can cause a hurricane in the US. Small change in pressure, disproportionate effect. This study of non-linear Physics became known as Chaos Theory.

Subtractive colour mixing: an experiment with watercolours

I've always wanted to be a painter so I succumbed to an impulse purchase of cheap watercolors over the summer. A spot of Youtube tuition later and here are the results. It turned out that the trick was to mix the colours together. It was many years ago that I first found out that Art and Science have different primary colours. In Physics, we start with darkness and add in coloured LIGHT. This is additive colour mixing where extra energy at different wavelengths is added to the spectrum. You can add in red, green and blue and you add these frequencies to get white. In Art, it's about what reflects back when you shine on white light. Or more to the point, what gets absorbed. That's why paint mixing is called SUBTRACTIVE colour mixing. Each pigment absorbs different frequencies and what's left gets reflected back. Now I know the theory I just need to get some talent ...

Offspring 1 at Yorkshire Sculpture Park

 I liked this fountain at Yorkshire Sculpture Park. It is convex about one axis which means that I look thinner laterally but am the same height as normal.

 I was interested that the water wasn't an even flow but was coming down in blobs with gaps between. The pump was making a steady hum which means that it was probably vibrating the whole fountain so that the flow from the reservoir down was not even.